the number system skill practice and problem solving

• Rating Count
• Price (Ascending)
• Price (Descending)
• Most Recent

The number system skill practice and problem solving

Resource type.

Solving Ratio Problems with Tape Diagrams Task Cards Practice Activity

Solving Systems of Linear Equations Color by Number Activity

Algebra 2 Regents Review Skills Packet

Real Numbers & Square and Cube Roots Scavenger Hunt Activity 8th grade math

7th Grade Math The Number System Review Classwork or Homework

6th Grade Math Common Core - Problem of the Day - Weeks 1-10 Bundle

Solving Systems of Equations by Substitution Isolated Expression Color by Number

6th Grade Number Systems : Long Division (6.NS.B.2)

Adding and Subtracting Integers Word Problems Practice for 7th Grade Math

Solar System Addition & Subtraction (within 10) Printable

Operations with Integers – 7th Grade Number System

BRIDGE TO ALGEBRA - REVIEW OF SKILLS NECESSARY FOR SUCCESS IN ALGEBRA

Adding and Subtracting Integers Practice for 7th Grade Math | Middle School

Systems of Equations Elimination: Secret Numbers

6th Grade Math Common Core - Problem of the Day - Weeks 6-10

Daily Math Practice Bundle for RIT Band 221 - 230

Daily Math Practice Bundle for RIT Band 211 - 220

Daily Math Practice for RIT Band 211 - 220 Set A

Solving Systems of Equations by Graphing, Substitution, and Elimination Activity

Daily Math Practice for RIT Band 231 - 240 Set A

Daily Math Practice for RIT Band 221 - 230 Set A

Solving Systems of Equations Color by Number *Differentiated*

8th Grade Math Activity - Full Year of 8th Grade Math Activities and Worksheets

Daily Math Practice for RIT Band 201 - 210 Set A

• We're hiring
• Help & FAQ
• Privacy policy
• Student privacy
• Terms of service
• Tell us what you think

Number Sense Worksheets

Welcome to the number sense page at Math-Drills.com where we've got your number! This page includes Number Worksheets such as counting charts, representing, comparing and ordering numbers worksheets, and worksheets on expanded form, written numbers, scientific numbers, Roman numerals, factors, exponents, and binary numbers. There are literally hundreds of worksheets meant to help students develop their understanding of numeration and number sense.

In the first few sections, there are some general use printables that can be used in a variety of situations. Hundred charts, for example, can be used for counting, but they can just as easily be used for learning decimal hundredths. Rounding worksheets help students learn this important skill that is especially useful in estimation.

Comparing and ordering numbers worksheets help students further understand place value and the ordinality of numbers. Continuing down the page are a number of worksheets on number forms: written, expanded, standard, scientific, and Roman numerals. Near the end of the page are a few worksheets for older students on factors, factoring, exponents and roots and binary numbers.

Most Popular Number Sense Worksheets this Week

Reading and Writing Numbers

There are a few different number posters in this section. The first two, with bird and butterfly themes include various ways of representing numbers from 0 to 9. Two versions of the numerals are used to demonstrate different printing styles, a Braille version and an American Sign Language version are also included to make students aware of different ways of representing each number. A linear representation and a ten-frame representation follow which is then followed by a pictorial representation using the theme. The poster sized numbers are just that ... made for printing and putting up in your classroom or home school.

• Number Recognition Posters Number Recognition Posters for 0 to 9 with a Bird Theme Number Recognition Posters for 0 to 9 with a Butterfly Theme
• Poster-Sized Numbers Poster sized numbers (black) Poster sized numbers (Outline) Poster sized numbers (Color)

Distinguishing between even and odd numbers is an important skill for young students to learn. The vocabulary of even and odd is used throughout their math education, so it is necessary to learn it as soon as possible. Connecting cubes can help a great deal in visually demonstrating odd and even numbers. Create the numbers from 1 to 10 (or more) using connecting cubes in pairs and students will quickly see that the odd numbers have an unpaired cube that can be thought of as the "odd cube out." Once they have seen this pattern, they may be able to extend the pattern without making cube models. Ask them about 11 and 12 and 35 and so on.

• Even and Odd Numbers Even and Odd Numbers Information Poster Count Circles and Determine Even or Odd Coloring Odd Numbers in a Grid Coloring Even Numbers in a Grid

In the writing numerals to 20 worksheets, you will find that the A version includes all numbers, B to E versions have about half the numbers included, F to I versions have about a third of the numbers included and the J version includes no numbers... just the lines to write them on. All versions include dashes under the numbers, so students have a reference for where to place the numbers. You can access the other versions (B to J) once you select the A version you want below.

• Practice Writing Numerals from 0 to 20 Write Numbers to 20 36pt Write Numbers to 20 60pt
• Practice Writing One Numeral at a Time Practice Writing the Numerals from 0 to 9 (36pt) Practice Writing the Numerals from 0 to 4 (36pt) Practice Writing the Numerals from 5 to 9 (36pt)

The main idea of learning to write numbers in words is to be able to say numbers correctly. In the past it might also have been useful for writing checks/cheques, but there isn't a lot of that going on any more. In writing, numbers up to ten are generally written as words and above ten as numerals. Numbers that are at the beginning of sentences are often written as words. These worksheets do not use the superfluous "and" throughout. If this is something you would like included, please send some feedback.

• Writing Small Numbers in Words Writing Numbers 0 to 10 in Words ✎ Writing Numbers 1 to 50 in Words ✎ Writing 2-digit Numbers in Words ✎ Writing 3-digit Numbers in Words ✎
• Writing Large Numbers in Words (Comma-Separated Thousands) Writing 4-digit Numbers in Words ✎ Writing 5-digit Numbers in Words ✎ Writing 6-digit Numbers in Words ✎ Writing 7-digit Numbers in Words ✎ Writing 8-digit Numbers in Words ✎ Writing 9-digit Numbers in Words ✎ Writing 5- to 9-digit Numbers in Words ✎ Writing 8- to 12-digit Numbers in Words ✎
• Writing Large Numbers in Words (Space-Separated Thousands) Writing 4-digit Numbers in Words (SI Number Format) ✎ Writing 5-digit Numbers in Words (SI Number Format) ✎ Writing 6-digit Numbers in Words (SI Number Format) ✎ Writing 7-digit Numbers in Words (SI Number Format) ✎ Writing 8-digit Numbers in Words (SI Number Format) ✎ Writing 9-digit Numbers in Words (SI Number Format) ✎ Writing 5- to 9-digit Numbers in Words (SI Number Format) ✎ Writing 8- to 12-digit Numbers in Words (SI Number Format) ✎

Now, let's see if students can write the numbers that are written! The reading numbers written as words worksheets do not have format options as the student question sheets are all written in words. The answer keys are formatted with a comma thousands separator when necessary.

• Reading Smaller Written Numbers Reading Written Two-Digit Numbers Reading Written Three-Digit Numbers
• Reading Larger Written Numbers Reading Written Four-Digit Numbers Reading Written Five-Digit Numbers Reading Written Six-Digit Numbers Reading Written Seven-Digit Numbers Reading Written Eight-Digit Numbers Reading Written Nine-Digit Numbers

Counting Worksheets

Ten frames help students visualize numbers in relation to 10. They are used for many purposes, but the worksheets below are introductory and familiarize students with ten frames and give them practice using them.

• Identify Ten Frames Identify Ten Frames with the Numbers in Order Identify Ten Frames with the Numbers in Reverse Order Identify Ten Frames with the Numbers in Random Order (10 versions)
• Draw Ten Frames Draw Ten Frames with the Numbers in Order Draw Ten Frames with the Numbers in Reverse Order Draw Ten Frames with the Numbers in Random Order (10 versions)

These skip counting worksheets include pictorial representations of the items the student is counting. For example, in the counting by 3's worksheet, students will see groups of three cars. This allows students to develop a mental image of skip counting. With larger numbers, including groups of items become impractical, so numbers are instead printed on the cars.

• Skip Counting by Numbers 1 to 10 Counting by 1's with Cars Skip Counting by 2's with Cars Skip Counting by 3's with Cars Skip Counting by 4's with Cars Skip Counting by 5's with Cars Skip Counting by 6's with Cars Skip Counting by 7's with Cars Skip Counting by 8's with Cars Skip Counting by 9's with Cars Skip Counting by 10's with Cars
• Skip Counting by Numbers Greater Than 10 Skip Counting by 11's with Cars Skip Counting by 12's with Cars Skip Counting by 25's with Cars Skip Counting by 50's with Cars Skip Counting by 100's with Cars

Hundred charts are useful not only for learning counting but for many other purposes in math. For example, a hundred chart can be used to model fractions and to convert fractions into decimals. Modeling 1/4 on a hundred chart would require coloring every fourth square. After coloring every fourth square, there would be 25 squares colored in which is 25/100 or 0.25. Not magic, just math. Hundred charts can also be used as graph paper for graphing, learning long multiplication and division or any other purpose. A common use for hundred charts in older grades is to use it to find prime and composite numbers using the sieve of Eratosthenes.

• Filled and Blank 100 Charts 100 Chart 100 Charts (4 Charts) Left-Handed 100 Chart Left-Handed 100 Charts (4 Charts) Blank 100 Chart ✎ Blank 100 Charts (4 Charts) ✎
• Partially Filled 100 Charts 100 Chart with Even Numbers ✎ 100 Chart with Odd Numbers ✎ 100 Chart with Multiples of 3 ✎ 100 Chart with Multiples of 4 ✎ 100 Chart with Multiples of 5 ✎ 100 Chart with Multiples of 6 ✎ 100 Chart with Multiples of 7 ✎ 100 Chart with Multiples of 8 ✎ 100 Chart with Multiples of 9 ✎ 100 Chart with Multiples of 10 ✎ Partially Completed 100 Chart (About 20%) ✎ Partially Completed 100 Charts (About 20%) (4 Charts) ✎

Have you ever thought about why hundred charts start at the top and count left to right and top to bottom? After all, don't we count UP rather than down? Thermometers have smaller numbers at the bottom, elevation increases the further you go up, and liquids fill from the bottom up. Coordinate grids have decreasing numbers going down and increasing numbers going up. Maybe starting with one at the bottom makes a lot more sense to students than starting with one at the top.

• Filled and Blank Bottom-Up 100 Charts Bottom-Up 100 Chart Bottom-Up 100 Chart Blank ✎
• Partially Filled Bottom-Up 100 Charts Bottom-Up 100 Chart with Even Numbers ✎ Bottom-Up 100 Chart with Odd Numbers ✎ Bottom-Up 100 Chart with Multiples of 3 ✎ Bottom-Up 100 Chart with Multiples of 4 ✎ Bottom-Up 100 Chart with Multiples of 5 ✎ Bottom-Up 100 Chart with Multiples of 6 ✎ Bottom-Up 100 Chart with Multiples of 7 ✎ Bottom-Up 100 Chart with Multiples of 8 ✎ Bottom-Up 100 Chart with Multiples of 9 ✎ Bottom-Up 100 Chart with Multiples of 10 ✎ Bottom-Up 100 Charts Partially Filled ✎

120 charts are very similar to hundred charts except they include the numbers from 101 to 120. 120 is a nice number for many reasons. One reason is that it has a lot of divisors—16 in fact. This makes the number 120 useful for many different grouping activities. Another reason is the Common Core Curriculum in the United States requires first graders to count to 120. A third reason is that 120 includes some three-digit numbers which could be a good introduction for some students into the hundreds place.

• Filled and Blank 120 Charts 120 Chart 120 Charts (4 Charts) Left-Handed 120 Chart Left-Handed 120 Charts (4 Charts) Blank 120 Chart ✎ Blank 120 Charts (4 Charts) ✎
• Partially Filled 120 Charts 120 Chart with Even Numbers ✎ 120 Chart with Odd Numbers ✎ 120 Chart with Multiples of 3 ✎ 120 Chart with Multiples of 4 ✎ 120 Chart with Multiples of 5 ✎ 120 Chart with Multiples of 6 ✎ 120 Chart with Multiples of 7 ✎ 120 Chart with Multiples of 8 ✎ 120 Chart with Multiples of 9 ✎ 120 Chart with Multiples of 10 ✎ Partially Completed 120 Chart (About 20%) ✎ Partially Completed 120 Charts (About 20%) (4 Charts) ✎

Similar to the bottom-up 100 charts, the bottom-up 120 charts start counting at the bottom and increase as you go up. Still not convinced that these make sense? Here are some more examples of things that start counting at the bottom: your height, snow depth, floors in a building, scales on most graphs, and altitude.

• Filled and Blank Bottom-Up 120 Charts Bottom-Up 120 Chart Bottom-Up 120 Chart Blank ✎
• Partially Filled Bottom-Up 120 Charts Bottom-Up 120 Chart with Even Numbers ✎ Bottom-Up 120 Chart with Odd Numbers ✎ Bottom-Up 120 Chart with Multiples of 3 ✎ Bottom-Up 120 Chart with Multiples of 4 ✎ Bottom-Up 120 Chart with Multiples of 5 ✎ Bottom-Up 120 Chart with Multiples of 6 ✎ Bottom-Up 120 Chart with Multiples of 7 ✎ Bottom-Up 120 Chart with Multiples of 8 ✎ Bottom-Up 120 Chart with Multiples of 9 ✎ Bottom-Up 120 Chart with Multiples of 10 ✎ Bottom-Up 120 Charts Partially Filled ✎

Ninety-nine charts include zero and have no three-digit numbers. Each row starts with a multiple of ten rather than ending with a multiple of ten.

• Filled and Blank 99 Charts 99 Chart 99 Charts (4 Charts) Left-Handed 99 Chart Left-Handed 99 Charts (4 Charts) Blank 99 Chart ✎ Blank 99 Charts (4 Charts) ✎
• Partially Filled 99 Charts 99 Chart with Even Numbers ✎ 99 Chart with Odd Numbers ✎ 99 Chart with Multiples of 3 ✎ 99 Chart with Multiples of 4 ✎ 99 Chart with Multiples of 5 ✎ 99 Chart with Multiples of 6 ✎ 99 Chart with Multiples of 7 ✎ 99 Chart with Multiples of 8 ✎ 99 Chart with Multiples of 9 ✎ 99 Chart with Multiples of 10 ✎ Partially Completed 99 Chart (About 20%) ✎ Partially Completed 99 Charts (About 20%) (4 Charts) ✎

You may not realize that many things start counting at zero, like when you are running around a track; you start at zero laps and count one for every lap you do. These charts start at zero at the bottom and go up to 99 at the top.

• Filled and Blank Bottom-Up 99 Charts Bottom-Up 99 Chart Bottom-Up 99 Chart Blank ✎
• Partially Filled Bottom-Up 99 Charts Bottom-Up 99 Chart with Even Numbers ✎ Bottom-Up 99 Chart with Odd Numbers ✎ Bottom-Up 99 Chart with Multiples of 3 ✎ Bottom-Up 99 Chart with Multiples of 4 ✎ Bottom-Up 99 Chart with Multiples of 5 ✎ Bottom-Up 99 Chart with Multiples of 6 ✎ Bottom-Up 99 Chart with Multiples of 7 ✎ Bottom-Up 99 Chart with Multiples of 8 ✎ Bottom-Up 99 Chart with Multiples of 9 ✎ Bottom-Up 99 Chart with Multiples of 10 ✎ Bottom-Up 99 Charts Partially Filled ✎

Counting collections of things in various patterns helps students develop shortcuts and strategies for counting. For example, when students count collections of items in rectangular patterns, they may use skip counting or multiplying to speed up their counting.

• Counting Animals Arranged in Patterns Counting Animals in Rectangular Patterns Counting Animals in Circular Patterns Counting Animals in Linear Patterns Counting Animals in Scattered Formations Counting Animals in Mixed Patterns Counting Animals in a Super Scatter (About 50 Percent Full) Counting Animals in a Super Scatter (100 Percent Full)

Counting and skip counting can be accomplished with number lines.

• Counting and Skip Counting on Number Lines Blank Number Lines Number Line to 100 by 1's Number Lines to 20 by 1's Number Lines to 40 by 2's Number Line to 200 by 2's Number Lines to 50 by 10's Number Line to 125 by 1's Number Line to 125 by 2's Number Line to 125 by 3's Number Line to 125 by 4's Number Line to 125 by 5's Number Line to 125 by 6's Number Line to 125 by 7's Number Line to 125 by 8's Number Line to 125 by 9's Number Line to 125 by 10's

A skill that is useful is to be able to continue counting or skip counting from any number.

• Continue Counting and Skip Counting From Various Numbers Continue Counting by 1 From Various Starting Numbers Continue Counting by 2 From Various Starting Numbers Continue Counting by 3 From Various Starting Numbers Continue Counting by 4 From Various Starting Numbers Continue Counting by 5 From Various Starting Numbers Continue Counting by 6 From Various Starting Numbers Continue Counting by 7 From Various Starting Numbers Continue Counting by 8 From Various Starting Numbers Continue Counting by 9 From Various Starting Numbers Continue Counting by 10 From Various Starting Numbers

Similar to the counting from any number worksheets, this one asks students to count down from different numbers.

• Continue Counting Backwards Counting Backwards with Numbers to 120 Starting at Random Numbers

Rounding Numbers Worksheets

Not only does rounding further an understanding of numbers, it can also be quite useful in estimating and measuring. There are many every day situations where a precise number isn't needed. For example if you needed to paint your basement floor, you don't really need to find out the area to exact square inch since you don't buy paint that way. You get a good idea of the floor space (e.g. it is roughly 20 feet by 15 feet) then read the label on the can to see how many square feet the can of paint covers (which, by the way is also a rounded number and variable depending on the roller used, the porosity of the floor, etc.) and buy enough cans to cover your floor.

• Rounding Numbers Rounding Numbers to Tens (Comma-Separated Thousands) Rounding Numbers to Hundreds (Comma-Separated Thousands) Rounding Numbers to Thousands (Comma-Separated Thousands) Rounding Numbers to Ten Thousands (Comma-Separated Thousands) Rounding Numbers to Hundred Thousands (Comma-Separated Thousands) Rounding Numbers to Millions (Comma-Separated Thousands)
• Canadian (SI) Format Rounding Numbers Rounding Numbers to Tens (Space-Separated Thousands) Rounding Numbers to Hundreds (Space-Separated Thousands) Rounding Numbers to Thousands (Space-Separated Thousands) Rounding Numbers to Ten Thousands (Space-Separated Thousands) Rounding Numbers to Hundred Thousands (Space-Separated Thousands) Rounding Numbers to Millions (Space-Separated Thousands)
• European Format Rounding Numbers Rounding Numbers to Tens (Period-Separated Thousands) Rounding Numbers to Hundreds (Period-Separated Thousands) Rounding Numbers to Thousands (Period-Separated Thousands) Rounding Numbers to Ten Thousands (Period-Separated Thousands) Rounding Numbers to Hundred Thousands (Period-Separated Thousands) Rounding Numbers to Millions (Period-Separated Thousands)

Comparing and Ordering/Sorting Numbers

There are many situations where it is important to know the relative size of one number to another. Several words are used to describe the relative sizes of one number to another, but it is probably best to use lesser than, greater than and equal to, although other words are more appropriate in certain situations. For example, if you were comparing two groups of candies, you would probably say, "there are fewer candies in that pile than in that one." The use of the word, "tight" , in the worksheet titles means the numbers to be compared are close to one another.

• Comparing Small Numbers Comparing Numbers to 9 Comparing Numbers to 25 Comparing Numbers to 50 Comparing Numbers to 50 (tight) Comparing Numbers to 100 Comparing Numbers to 100 (tight) Comparing Numbers to 1000 Comparing Numbers to 1000 (tight)
• Comparing Large Numbers Comparing Numbers to 10,000 (Comma-Separated Thousands) Comparing Numbers to 10,000 (tight) (Comma-Separated Thousands) Comparing Numbers to 100,000 (Comma-Separated Thousands) Comparing Numbers to 100,000 (tight) (Comma-Separated Thousands) Comparing Numbers to 1,000,000 (Comma-Separated Thousands) Comparing Numbers to 1,000,000 (tight) (Comma-Separated Thousands) Comparing Numbers to 10,000,000 (Comma-Separated Thousands) Comparing Numbers to 10,000,000 (tight) (Comma-Separated Thousands)
• Canadian (SI) Format Comparing Large Numbers Comparing Numbers to 10 000 (Space-Separated Thousands) Comparing Numbers to 10 000 (tight) (Space-Separated Thousands) Comparing Numbers to 100 000 (Space-Separated Thousands) Comparing Numbers to 100 000 (tight) (Space-Separated Thousands) Comparing Numbers to 1 000 000 (Space-Separated Thousands) Comparing Numbers to 1 000 000 (tight) (Space-Separated Thousands) Comparing Numbers to 10 000 000 (Space-Separated Thousands) Comparing Numbers to 10 000 000 (tight) (Space-Separated Thousands)
• European Format Comparing Large Numbers Comparing Numbers to 10.000 (Period-Separated Thousands) Comparing Numbers to 10.000 (tight) (Period-Separated Thousands) Comparing Numbers to 100.000 (Period-Separated Thousands) Comparing Numbers to 100.000 (tight) (Period-Separated Thousands) Comparing Numbers to 1.000.000 (Period-Separated Thousands) Comparing Numbers to 1.000.000 (tight) (Period-Separated Thousands) Comparing Numbers to 10.000.000 (Period-Separated Thousands) Comparing Numbers to 10.000.000 (tight) (Period-Separated Thousands)
• Sorting/Ordering Small Numbers Ordering Numbers from 0 to 9 Ordering Numbers from 1 to 20 Ordering Numbers from 10 to 50 Ordering Numbers from 10 to 99 Ordering Numbers from 100 to 999

Converting Numbers to Different Forms

When writing numbers in expanded form, students might use one of three forms which will be demonstrated using the number 9753. The first form is quite simple and combines both the place and the place value. For example, 9 is in the thousands place which means the value of that 9 is 9000. The 7 is in the hundreds place which makes it 700. The 5 is in the tens place which makes it 50 and the 3 is in the ones place which makes it 3.

To write in "simple" expanded form , simply separate these four values with plus signs: 9000 + 700 + 50 + 3.

In expanded factors form , the place and the place value are separated with multiplication signs: (9 × 1000) + (7 × 100) + (5 × 10) + (3 × 1). Parentheses are included for clarity.

In expanded exponential form , the place values are expressed as powers of ten: (9 × 10 3 ) + (7 × 10 2 ) + (5 × 10 1 ) + (3 × 10 0 ).

• Converting Standard Form Numbers to Expanded Form Converting 3-Digit Standard Form Numbers to Expanded Form Converting 4-Digit Standard Form Numbers to Expanded Form Converting 5-Digit Standard Form Numbers to Expanded Form Converting 6-Digit Standard Form Numbers to Expanded Form Converting 7-Digit Standard Form Numbers to Expanded Form Converting 8-Digit Standard Form Numbers to Expanded Form Converting 9-Digit Standard Form Numbers to Expanded Form
• Converting Standard Form Numbers to Expanded Factors Form Converting 3-Digit Standard Form Numbers to Expanded Factors Form Converting 4-Digit Standard Form Numbers to Expanded Factors Form Converting 5-Digit Standard Form Numbers to Expanded Factors Form Converting 6-Digit Standard Form Numbers to Expanded Factors Form Converting 7-Digit Standard Form Numbers to Expanded Factors Form Converting 8-Digit Standard Form Numbers to Expanded Factors Form Converting 9-Digit Standard Form Numbers to Expanded Factors Form
• Converting Standard Form Numbers to Expanded Exponential Form Converting 3-Digit Standard Form Numbers to Expanded Exponential Form Converting 4-Digit Standard Form Numbers to Expanded Exponential Form Converting 5-Digit Standard Form Numbers to Expanded Exponential Form Converting 6-Digit Standard Form Numbers to Expanded Exponential Form Converting 7-Digit Standard Form Numbers to Expanded Exponential Form Converting 8-Digit Standard Form Numbers to Expanded Exponential Form Converting 9-Digit Standard Form Numbers to Expanded Exponential Form
• Converting Expanded Form Numbers to Standard Form Converting 3-Digit Expanded Form Numbers to Standard Form Converting 4-Digit Expanded Form Numbers to Standard Form Converting 5-Digit Expanded Form Numbers to Standard Form Converting 6-Digit Expanded Form Numbers to Standard Form Converting 7-Digit Expanded Form Numbers to Standard Form Converting 8-Digit Expanded Form Numbers to Standard Form Converting 9-Digit Expanded Form Numbers to Standard Form
• Converting Expanded Factors Form Numbers to Standard Form Converting 3-Digit Expanded Factors Form Numbers to Standard Form Converting 4-Digit Expanded Factors Form Numbers to Standard Form Converting 5-Digit Expanded Factors Form Numbers to Standard Form Converting 6-Digit Expanded Factors Form Numbers to Standard Form Converting 7-Digit Expanded Factors Form Numbers to Standard Form Converting 8-Digit Expanded Factors Form Numbers to Standard Form Converting 9-Digit Expanded Factors Form Numbers to Standard Form
• Converting Expanded Exponential Form Numbers to Standard Form Converting 3-Digit Expanded Exponential Form Numbers to Standard Form Converting 4-Digit Expanded Exponential Form Numbers to Standard Form Converting 5-Digit Expanded Exponential Form Numbers to Standard Form Converting 6-Digit Expanded Exponential Form Numbers to Standard Form Converting 7-Digit Expanded Exponential Form Numbers to Standard Form Converting 8-Digit Expanded Exponential Form Numbers to Standard Form Converting 9-Digit Expanded Exponential Form Numbers to Standard Form

These versions use a space as a thousands separator.

• Canadian (SI) Format Converting Standard Form Numbers to Expanded Form Writing 5-Digit Numbers in Expanded Form (Space-Separated Thousands) Writing 6-Digit Numbers in Expanded Form (Space-Separated Thousands) Writing 7-Digit Numbers in Expanded Form (Space-Separated Thousands) Writing 8-Digit Numbers in Expanded Form (Space-Separated Thousands) Writing 9-Digit Numbers in Expanded Form (Space-Separated Thousands) (Retro) Write Expanded Form (range 1 000 to 9 999) (Space-Separated Thousands)

These versions use a period as a thousands separator.

• European Format Converting Standard Form Numbers to Expanded Form Writing 5-Digit Numbers in Expanded Form (Period-Separated Thousands) Writing 6-Digit Numbers in Expanded Form (Period-Separated Thousands) Writing 7-Digit Numbers in Expanded Form (Period-Separated Thousands) Writing 8-Digit Numbers in Expanded Form (Period-Separated Thousands) Writing 9-Digit Numbers in Expanded Form (Period-Separated Thousands) (Retro) Write Expanded Form (range 1.000 to 9.999) (Period-Separated Thousands)

The standard, expanded and written forms conversion worksheets include three number forms on the same page.

• Converting Between Standard, Expanded and Written Form Numbers Converting Between Standard, Expanded and Written Forms ( 3-Digit ) Converting Between Standard, Expanded and Written Forms ( 4-Digit ) Converting Between Standard, Expanded and Written Forms (5-Digit) Converting Between Standard, Expanded and Written Forms (3-Digit to 5-Digit) Converting Between Standard, Expanded and Written Forms (6-Digit) Converting Between Standard, Expanded and Written Forms (7-Digit) Converting Between Standard, Expanded and Written Forms (8-Digit) Converting Between Standard, Expanded and Written Forms (9-Digit) Converting Between Standard, Expanded and Written Forms (6-Digit to 9-Digit)
• Canadian (SI) Format Converting Between Standard, Expanded and Written Form Numbers Converting Between Standard, Expanded and Written Forms (5-Digit; Space-Separated Thouands) Converting Between Standard, Expanded and Written Forms (3-Digit to 5-Digit; Space-Separated Thouands) Converting Between Standard, Expanded and Written Forms (6-Digit; Space-Separated Thouands) Converting Between Standard, Expanded and Written Forms (7-Digit; Space-Separated Thouands) Converting Between Standard, Expanded and Written Forms (8-Digit; Space-Separated Thouands) Converting Between Standard, Expanded and Written Forms (9-Digit; Space-Separated Thouands) Converting Between Standard, Expanded and Written Forms (6-Digit to 9-Digit; Space-Separated Thouands)
• Convert Numbers in Standard Form to Scientific Notation Convert Standard to Scientific Notation (Large Numbers Only) Convert Standard to Scientific Notation (Small Numbers Only) Convert Standard to Scientific Notation (Large and Small Numbers)
• Convert Numbers in Scientific Notation to Standard Form Convert Scientific to Standard Numbers (Large Numbers Only) Convert Scientific to Standard Numbers (Small Numbers Only) Convert Scientific to Standard Numbers (Large and Small Numbers)
• Convert Numbers Between Standard Form and Scientific Notation Convert Between Standard and Scientific Numbers (Large Numbers Only) Convert Between Standard and Scientific Numbers (Small Numbers Only) Convert Between Standard and Scientific Numbers (Large and Small Numbers)

This is about as "old school" as you can get. Put on your tunic and pick up your scutum to tackle the worksheets on Roman Numerals. Below, you will see options for standard and compact forms. The standard form Roman Numeral math worksheets include numerals in the commonly-taught version where 999 is CMXCIX (i.e. write the numeral one place value at a time). The compact versions are for those who want more of a challenge where the Roman numerals are written in as concise a version as possible. In the compact version, 999 is written as IM (i.e. one less than 1000).

• Converting Roman Numerals to Standard Form Numbers Converting Roman Numerals up to X (10) to Standard Numbers Converting Roman Numerals up to C (100) to Standard Numbers Converting Roman Numerals up to M (1000) to Standard Numbers Converting Roman Numerals up to MMMCMXCIX (3999) to Standard Numbers
• Converting Compact Roman Numerals to Standard Form Numbers Compact Roman Numerals up to C Compact Roman Numerals up to M Compact Roman Numerals up to MMMIM

Operations with Roman numerals

• Adding Roman Numerals Adding Roman Numerals up to XXV Adding Roman Numerals up to C Adding Roman Numerals up to M Adding Roman Numerals up to MMMCMXCIX
• Subtracting Roman Numerals Subtracting Roman Numerals up to XXV Subtracting Roman Numerals up to C Subtracting Roman Numerals up to M Subtracting Roman Numerals up to MMMCMXCIX
• Multiplying Roman Numerals Multiplying Roman Numerals up to C Multiplying Roman Numerals up to M Multiplying Roman Numerals up to MMMCMXCIX
• Dividing Roman Numerals Dividing Roman Numerals up to C Dividing Roman Numerals up to M Dividing Roman Numerals up to MMMCMXCIX
• Mixed Operations With Roman Numerals Mixed Operations with Roman Numerals up to C Mixed Operations with Roman Numerals up to M Mixed Operations with Roman Numerals up to MMMCMXCIX

Factors and Factoring

What would factoring be without some factoring trees? They are probably the most elegant and convenient way to find the prime factors of a number, but they take a little practice, which is where we come in. The worksheets below are of two types. The first is finding all of the factors of a number. This is great for students who know their multiplication/division facts. If they don't, they might find this a little frustrating, so go back and work on that first. The second type is finding prime factors which we've chosen to do with tree diagrams. Among other things, this is a great way to find prime numbers and to practice divisibility rules.

• Lists of Factors List of Factors of Numbers 2 to 99 (Informational) List of Factors of Numbers 100 to 999 (Informational) List of Factors of Numbers 1000 to 9999 (Informational; CAUTION 166 Pages)
• Determining Factors of Numbers Determining Factors of Numbers (range 4 to 50) Determining Factors of Numbers (range 50 to 100) Determining Factors of Numbers (range 100 to 200) Determining Factors of Numbers (range 200 to 400)
• Lists of Prime Factors List of Prime Factors of Numbers 2 to 99 (Informational) List of Prime Factors of Numbers 100 to 999 (Informational) List of Prime Factors of Numbers 1000 to 9999 (Informational; CAUTION 137 Pages)
• Determining Prime Factors Using a Tree Diagram Determining Prime Factors Using a Tree Diagram (range 4 to 48) Determining Prime Factors Using a Tree Diagram (range 4 to 96) Determining Prime Factors Using a Tree Diagram (range 4 to 144) Determining Prime Factors Using a Tree Diagram (range 48 to 192) Determining Prime Factors Using a Tree Diagram (range 48 to 240)
• Calculating Greatest Common Factor Using Prime Factors Calculating Greatest Common Factors Using Prime Factors ; Range 4 to 100 (Sets of 2) Calculating Greatest Common Factors Using Prime Factors ; Range 100 to 200 (Sets of 2) Calculating Greatest Common Factors Using Prime Factors ; Range 200 to 400 (Sets of 2) Calculating Greatest Common Factors Using Prime Factors ; Range 4 to 400 (Sets of 2)
• Determining Greatest Common Factor Using All Factors Determining Greatest Common Factors Using All Factors ; Range 4 to 100 (Sets of 2) Determining Greatest Common Factors Using All Factors ; Range 100 to 200 (Sets of 2) Determining Greatest Common Factors Using All Factors ; Range 200 to 400 (Sets of 2) Determining Greatest Common Factors Using All Factors ; Range 4 to 400 (Sets of 2)

Least Common Multiple (LCM) Worksheets

• Determine Least Common Multiple from Multiples Determine LCM From Multiples of Numbers to 10 (LCM Not One of the Numbers or the Product) Determine LCM From Multiples of Numbers to 10 (LCM Not One of the Numbers) Determine LCM From Multiples of Numbers to 10 Determine LCM From Multiples of Numbers to 15 (LCM Not One of the Numbers or the Product) Determine LCM From Multiples of Numbers to 15 (LCM Not One of the Numbers) Determine LCM From Multiples of Numbers to 15 Determine LCM From Multiples of Numbers to 25 (LCM Not One of the Numbers or the Product) Determine LCM From Multiples of Numbers to 25 (LCM Not One of the Numbers) Determine LCM From Multiples of Numbers to 25
• Determine Least Common Multiple from Prime Factors Determine LCM From Prime Factors of Numbers to 25 (LCM Not One of the Numbers or the Product) Determine LCM From Prime Factors of Numbers to 50 (LCM Not One of the Numbers or the Product) Determine LCM From Prime Factors of Numbers to 100 (LCM Not One of the Numbers or the Product)

Exponents and Roots

• Squares of Numbers Squares of Numbers from 0 to 9 Squares of Numbers from 1 to 12 Squares of Numbers from 1 to 20 Common Squares (Squares of 1 to 15, 20, 25, and multiples of 10 to 90) Squares of Numbers from 1 to 32 Squares of Numbers from 1 to 99
• Square Roots Square Roots 0 to 9 Square Roots 1 to 12 Square Roots 1 to 20 Common Square Roots (1 to 15, 20, 25, and multiples of 10 to 90) Square Roots 1 to 32 Square Roots 1 to 99
• Squares and Square Roots Mixed Squares and Square Roots of Numbers 1 to 16 Squares and Square Roots of Common Numbers (1 to 15, 20, 25, and multiples of 10 to 90)
• Cubes of Numbers Cubes of Numbers from 0 to 9 Cubes of Numbers from 1 to 12 Cubes of Numbers from 1 to 20 Cubes of Numbers from 1 to 32
• Cube Roots Cube Roots 0 to 9 Cube Roots 1 to 12 Cube Roots 1 to 20 Common Cube Roots (1 to 15, 20, 25, and multiples of 10 to 90) Cube Roots 1 to 32 Cube Roots 1 to 99
• Cubes and Cube Roots Cubes and Cube Roots
• Exponents in Factor Form Exponents in Factor Form

Other Base Number Systems

The binary number system has broad applications, but it is most known for its predominance in computer architecture. Learning about the binary system not only encourages higher order thinking, but it also prepares students for further studies in mathematics and computer studies. The chart below may be useful for students who need some help lining things up and learning about place value as it relates to the binary system. We included a base 10 number column, so you can use the chart for converting between decimal and binary systems.

• Binary Place Value Chart Binary Place Value Chart

The mystery number trick below is actually based on binary numbers. As you may know, each place in the binary system is a power of 2 (1, 2, 4, 8, 16, etc.). Since every decimal (base 10) number can be expressed as a binary number, each decimal number can therefore be expressed as a sum of a unique set of powers of 2. It is this concept that makes this trick work. You might notice that the largest decimal number on the cards is 63 which is also the largest 6-digit binary number (111111). The target position on each version of the mystery number trick contains the powers of 2 associated with the first 6 place values in the binary system (1, 2, 4, 8, 16, 32). Each of the 6 cards represents a specific place value. All 32 numbers on each card contain a 1 in the associated place when written in binary. Basically, when the "friend" identifies the cards that contain the mystery number, they are giving you a binary number that simply needs converting into a decimal number. Just for fun, we mixed up the numbers on the cards and the target position on versions C to J. Version A includes numbers in ascending order and version B includes numbers in descending order. The other versions (B to J) will be available once you click on the A version below.

• Binary Mystery Number Trick Mystery Number Trick
• Converting from Decimal Numbers to Other Base Number Systems Converting from Decimal to Binary Converting from Decimal to Octal Converting from Decimal to Hexadecimal Converting from Decimal to Various Other Base Sytems
• Converting from Binary Numbers to Other Base Number Systems Converting from Binary to Decimal Converting from Binary to Octal Converting from Binary to Hexadecimal Converting from Binary to Various Other Base Sytems
• Converting from Octal Numbers to Other Base Number Systems Converting from Octal to Decimal Converting from Octal to Binary Converting from Octal to Hexadecimal Converting from Octal to Various Other Base Sytems
• Converting from Hexadecimal Numbers to Other Base Number Systems Converting from Hexadecimal to Decimal Converting from Hexadecimal to Binary Converting from Hexadecimal to Octal Converting from Hexadecimal to Various Other Base Sytems
• Converting from Various Base Numbers to Other Base Number Systems Converting from Various Base Systems to Decimal Converting from Various Base Systems to Binary Converting from Various Base Systems to Octal Converting from Various Base Systems to Hexadecimal Converting Between Various Base Systems

Help with Converting Between Base Number Systems:

There are shortcuts for converting between some bases. For example, converting from binary to octal takes little effort since 8 is a power of 2. Each group of 3 digits in a binary number represents a single digit in an octal number. For example, 111 2 (the 2 stands for binary or base 2) is 7 8 (the 8 stands for octal or base 8). The simple way to convert binary numbers to octal numbers is to group the binary number into groups of three digits. For example, 111010101000111 2 could be written as 111 010 101 000 111. Converting each group into octal means multiplying the first digit of each group by 4, the second digit by 2 and the third digit by 1 then adding the results together. This will result in digits no larger than 7 (since 4 + 2 + 1 = 7) and the number will be converted to base 8. In octal, therefore, the number is 72507 8 . If you can express the octal numbers from 0 to 7 in binary, you can easily convert the other way. For example 7223 8 = 111010010011 2 since 7 is 111, 2 is 010, and 3 is 011 in binary.

A similar shortcut for converting between binary and base 4 numbers involves looking at binary numbers in groups of 2. Similarly, converting from base 3 to base 9 and base 4 to base 16 involves groups of two. Converting from binary to hexadecimal would involve groups of 4.

For other conversions, a commonly used tactic is to convert to decimal as an intermediate step since this is the base system that is probably ingrained in your brain, so it is much more intuitive. For example, converting from a base 5 number to a base 7 number would involve first converting the base 5 number to base 10. To convert, it is only necessary to know the place values of the system that you are converting from and to. In base 5, the lowest place value (furthest to the right) of whole numbers is 1 followed by 5, 25, 125 and so on. In base 7, the place values are 1, 7, 49, 343 and so on. First multiply the digits in the base 5 number by its place values, then divide the resulting decimal number by the base 7 place values and you will have your conversion. For example 4331 5 is expanded to (4 × 125) + (3 × 25) + (3 × 5) + (1 × 1) = 500 + 75 + 15 + 1 = 591 (in base 10). To continue into base 7, there are at least two ways, the second method is in the next paragraph. For simplicity's sake, take the largest base 7 place value that will divide into 591 at least once. In this case it is 343 which goes into 591 exactly once (1) with a remainder of 248. Divide the remainder by the next place value down, 49, to get (5) with a remainder of 3. Divide 3 by 7 which is (0) with a remainder of 3. Finally, divide by 1 which should leave no remainder, and it is (3) in this case. Put all those digits together and you should have your number in base 7: 1503 7 .

A method to convert directly from one base system to another involves knowing how to divide in the base system you want to convert from. It is fairly easy if you are familiar with the base system. Simply divide the number by the base you want to convert to (but express it in the original base system). Repeat until the division results in 0 with or without a remainder. Convert the remainders and put them in reverse order for the number in the new base system. For example, convert 3750 8 to hexadecimal (base 16). 16 in base 8 is 20 8 . The first step is to divide 3750 8 by 20 8 = 176 8 R 10 8 . Next, divide 176 8 by 20 8 to get 7 8 R 16 8 . Finally, 7 8 divided by 20 8 is 0 8 R 7 8 . Convert the remainders to base 16 (which you may have to think of in terms of decimal numbers, or you can use your fingers and some toes) and write the digits in reverse order. 7 8 is 7 16 , 16 8 is (14 in decimal) E 16 , and 10 8 is 8 16 . So, the number 3750 8 is 7A8 16 .

Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

In order to access this I need to be confident with:

Number sense

Here you will learn about number sense, including what it is and different ways to develop it.

Students will first learn about number sense from the beginning of their experiences with numbers and they continue to build on this knowledge throughout all experiences in math.

What is number sense?

Number sense is the ability to think flexibly and critically about numbers and their operations.

Someone with a strong number sense can…

• Solve or make reasonable estimates using mental math.
• Represent numbers or solve operations in more than one way.
• Make connections between solving strategies.

Number sense is not a “check the box” kind of skill. Each student lies somewhere on the spectrum of number sense, and with each mathematical experience there is an opportunity to build a deeper understanding or “sense of number.”

Number sense is embedded into any work with numbers and operations. This page will specifically cover whole numbers and the operations of addition and subtraction.

In young learners, building number sense around addition and subtraction may look like:

• Ask students to represent the number 8 in as many ways as they can. Then let students explain and compare their representations with others.

As students progress in their number sense and are ready to begin operating with numbers, activities may look like:

For example,

• Ask first grade students to compare the numbers 23 and 33 in more than one way. Then let students explain their comparisons with others. Then ask students how they could apply other students’ strategies to compare 33 and 43.
• Ask 2 nd grade students to subtract 83-59 mentally. Then ask students to share their thinking, while dictating their strategy on the board. Prompt students to make connections between the strategies they see being shared.
• Ask 3 rd grade students what number bond can help them solve 400-150. Then ask them how the same number bond could also help them solve 401-151 and 399-149. Encourage students to journal about their strategies or share them with other classmates.

[FREE] Arithmetic Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of arithmetic. 10+ questions with answers covering a range of 4th, 5th and 6th grade arithmetic topics to identify areas of strength and support!

Common Core State Standards

How does this relate to 1 st grade math, 2 nd grade math and 3 rd grade math?

• Grade 1 – Numbers and Operations in Base 10 (1.NBT.B.2) Understand that the two digits of a two-digit number represent amounts of tens and ones.
• Grade 2 – Numbers and Operations in Base 10 (2.NBT.B.5) Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
• Grade 3 – Numbers and Operations in Base 10 (3.NBT.A.1) Use place value understanding to round whole numbers to the nearest 10 or 100.
• Grade 3 – Numbers and Operations in Base 10 (3.NBT.A.2) Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

How to develop number sense

In order to develop number sense:

Create mental strategies for thinking about numbers and operations.

Practice representing strategies in more than one way.

Share strategies and listen to the strategies of others, comparing and contrasting.

Number sense examples

Example 1: understanding tens and ones.

How many tens and ones are in the number 27?

• Create mental strategies for thinking about numbers and operations. 

Picture 27 hearts in your head for a moment… How do you see them?

Maybe you see a straight line of 27…

Maybe you see 27 in groups, like in five frames…

Maybe you see 27 in groups, like in ten frames…

There are many different ways to “see” 27 in your head.

There is not a “wrong” way to picture 27, but notice which ways make it easier to understand 27 as a quantity.

2 Practice representing strategies in more than one way.

Now, think about different ways to show 27 with base 10 blocks.

Maybe you show 27 ones…

Maybe you show 1 ten and 17 ones…

Maybe you show 2 tens and 7 ones…

There are many ways to group 27, but notice which ways make it easier to understand 27 as a quantity.

3 Share strategies and listen to the strategies of others, comparing and contrasting.

Looking at all the strategies above, what is similar? What is different? Did you think of 27 in another way?

Example 2: add within 100

Solve 33 + 48.

Combine 33 and 48 in your head… How did you add the numbers?

Maybe you started at 33 and counted up 48 \text{:}

34, \, 35, \, 36, \, 37, \, 38, \, 39, \, 40, \, 41, \, 42….

Maybe you grouped the tens and the ones:

30 + 40 = 70 , and 3 + 8 = 11 .

So now you can add 70 + 11.

Maybe you broke apart 33 to make a ten:

= (31 + 2) + 48

= 31 + (2 + 48)

Grouping the 2 + 48 together makes 50, so now you can solve 31 + 50.

There are many ways to mentally solve 33 + 48, but notice which makes the most sense to you.

One way to represent 33 + 48 is with base 10 blocks.

Another way is to use a hundreds chart.

You can also create hops on a number line:

There are many ways to represent 33 + 48, but notice which makes the most sense to you.

Looking at all the strategies above, what is similar? What is different? Would you solve 33 + 48 a different way?

Example 3: subtract within 100

Solve 84 - 68.

Take 68 away from 84 in your head… How did you subtract the numbers?

Maybe you started at 68 and counted up 84 \text{:}

69, \, 70, \, 71, \, 72, \, 73, \, 74, \, 75, \, 76, \, 77….

Maybe you started at 68 and counted up by groups of ones and tens:

From 68 to 70 is 2.

From 70 to 84 is 14 more.

So the distance from 68 to 84 is 16.

Maybe you broke apart 68 to subtract each place value:

84 - 60 = 24

24 - 8 = 16

Something to think about: There are many ways to mentally solve 84 - 68, but notice which makes the most sense to you.

One way to represent 84 - 68 is with base 10 blocks.

There are many ways to represent 84 - 68, but notice which makes the most sense to you.

Looking at all the strategies above, what is similar? What is different? Would you solve 84 - 68 a different way?

How to develop specific number sense strategies

In order to develop specific number sense strategies:

Decide if making \textbf{10} or using number bonds can help you solve.

Solve with your strategy and explain why it works.

Example 4: subtract within 20

Solve 16 - 7.

Number bonds help you use what you know about addition to solve subtraction.

Think about what number plus 7 is equal to 16 to complete the number bond.

Since 9 completes the number bond, it is the difference between 16 and 7.

16 - 7 = 9.

Example 5: add within 100

Solve 34 + 37.

It is not always easy to remember larger number bonds, but you can make 10.

Think about how you can regroup part of 34 with 37 to make a multiple of 10.

= (31 + 3) + 37

= 31 + (3 + 37) \quad *You can regroup 3 to go with 37.

So, 34 + 37 = 71.

Example 6: subtract within 1,000

Solve 300 - 150.

Sometimes you can use smaller number bonds, to help solve operations with larger numbers.

Think about what number plus 15 is equal to 30 to complete the number bond.

Since 15 completes the number bond, the difference between 30 and 15 is 15. Since 300 and 150 are 10 times larger, their difference is also 10 times larger.

So, 300 - 150 = 150.

Teaching tips for number sense

• Do your best to embed number sense activities into all math lessons and through all math centers, math skills and math problems. This does not require extensive extra planning – instead always look for ways for students to solve problems in multiple ways, explain their problem solving (written or orally) and critique the strategies of others.
• Many activities will naturally lend themselves to building number sense, particularly activities with real-life contexts, the use of hands-on manipulatives, and a classroom emphasis on problem-solving. While not always appropriate, worksheets that encourage students to solve in more than one way or analyze the thinking of others can also be useful.

Easy mistakes to make

• Thinking that children need to be a certain year old to develop number sense Even before students can formally use numerals or other number symbols, they can develop their sense of number. Some activities for pre-k students might include subitizing (recognizing the number of objects without counting), identifying more and less when comparing two groups of objects or learning to count using number words.
• Teaching algorithms too quickly Introducing algorithms before students have had time to explore a topic and grapple with their own ideas can eliminate a student’s motivation, creativity, and ownership and encourage memorization of rules over understanding. While there is no hard and fast rule as to how to progress a topic, be mindful in giving students time to develop ideas and remember that building foundational understanding takes time.
• Requiring students to use specific number sense strategies Unless directed by your state standards to do so, it is not necessary to insist that students use a certain strategy or ask students to memorize a strategy. While this is often done with good intentions, it is similar to asking students to memorize or use an algorithm too quickly. The best way to promote the use of number sense within the classroom is to use activities that allow students to solve in more than one way and consistently ask students to talk about their strategies. It is also helpful to promote a growth mindset and help students see the value in admitting to and learning from their mistakes.

Related arithmetic lessons

• Skip counting
• Inverse operations
• Two step word problems
• Money word problems
• Calculator skills

Practice number sense questions

1) Which choice is NOT equal to 36?

3 tens and 6 ones

26 ones and 1 ten

6  ones and 30 tens

2 tens and 16 ones

The model above shows 6 ones and 30 tens, which is NOT equal to 36.

It is equal to 306.

2) Solve 18-11.

There are many ways to solve 18-11. Two ways are with a model and by using a number bond.

Show the tens and ones in 18 with a model and then subtract 11 \text{:}

Use a number bond to solve.

Both ways show that 18-11 = 7.

3) Solve 46 + 19.

There are many ways to solve 46 + 19. Two ways are with a model and by making 10.

Show the tens and ones with a model and then combine them:

Regroup 46 to make a multiple of 10.

= (45 + 1) + 19

= 45 + (1 + 19)

4) Which strategy does NOT show 18 + 27?

“18 = 3 + 15, so I add 27 + 3 = 30 and then 30 + 15.”

“I started at 27 and counted up 18.”

This model shows 1 + 8 + 2 + 7 which is NOT the same as 18 + 27.

A correct model for 18 + 27 is shown below.

*Note: Other models can also be used to show 18 + 27, but all correct models show a total of 45.

5) Which strategy does NOT show 35 + 26?

“26 = 5 + 21, so I add 35 + 5 = 30 and then 30 + 21.”

“I started at 35 and counted up 26.”

There is a mistake in this explanation:

35 + 5 = 40, so the correct strategy is:

= 35 + (5 + 21)

= (35 + 5) + 21

*Note that this strategy, making 10, can also be used with different numbers.

6) Solve 600-200.

There are many ways to solve 600-200. Two ways are with a model and by using a number bond.

Show the hundreds in 600 with a model and then subtract 200 \text{:}

2 + 4 = 6, so 200 + 400 = 600, since the numbers in the bond are 100 times larger.

Both ways show that 600-200 = 400.

Number sense FAQs

Success in mathematics depends on a deep understanding of numbers. How students learn math can impact the level of this understanding. A focus on developing number sense in elementary school promotes flexible thinking around whole numbers, fractions and decimals. This type of knowledge helps students understand concepts more deeply and encourages creative approaches to problem solving. This is particularly important as math topics become more abstract in middle school and high school. Students who have greater number sense are often more successful at applying what they know to new and more complex mathematics.

For younger students, much of their development of number sense comes from activities that involve math facts. This includes (but is not limited to) opportunities to solve with models and drawings, solving real-world problems that involve basic math facts, solving math facts mentally and sharing and critiquing solving strategies with others. For older students, math facts can be a tool utilized to solve complex problems more efficiently.

The next lessons are

• Properties of equality
• Addition and subtraction
• Multiplication and division

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

Find out how we can help your students achieve success with our math tutoring programs .

[FREE] Common Core Practice Tests (3rd to 8th Grade)

Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.

Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!

Privacy Overview

Number Sense in Math – Definition, Examples, Facts

What is number sense in math, essential elements in number sense, how to teach number sense, solved examples on number sense, practice problems on number sense, frequently asked questions on number sense.

Number sense refers to a person’s ability to work with numbers, understand their quantities, and use them in meaningful ways. It encompasses the understanding of concepts like comparing numbers, determining their values, and recognizing their significance in various contexts.

In early childhood, number sense starts developing naturally as children make simple comparisons, such as choosing a larger piece of cake or understanding when something is taken away. These experiences lay the foundation for understanding addition and subtraction.

As educators and caregivers, we play a crucial role in helping children build a strong number sense by connecting these early experiences to a deeper understanding of numbers. By guiding children to comprehend what numbers represent, how they relate to one another, and their relevance in everyday life, we can support their overall mathematical development.

So, let’s dive into the fascinating world of number sense and explore how it shapes a child’s mathematical understanding and growth.

Recommended Games

Definition of Number Sense

Number sense, as defined by Gersten and Chard (prominent researchers in the field of Education) refers to a child’s fluidity and adaptability with numbers. It involves understanding the meaning of numbers, performing mental arithmetic operations, and making comparisons to comprehend the world around them.

Numbers can be represented using symbols, such as 1, 2, 3, or written in words, like one, two, three, and so on. Developing number sense begins with recognizing these symbols and understanding the corresponding numerical values.

To gain a strong number sense, children need to grasp the components that contribute to their understanding of numbers. Let’s explore these components in detail and uncover the building blocks of number sense.

Recommended Worksheets

More Worksheets

Number sense refers to a wide range of math skills. Here are some important components of number sense:

• Counting and Cardinality : Understanding counting, number sequences, and assigning numbers to objects.
• Quantity and Magnitude : Grasping quantity concepts and comparing/estimating quantities.
• Number Relationships : Recognizing patterns, understanding place value, and identifying number families.
• Operations and Computation : Performing mental calculations, solving arithmetic problems, and mastering basic operations.
• Estimation and Approximation : Making reasonable guesses and rounding numbers to specific values.
• Spatial Sense and Number Patterns : Identifying patterns in numbers, shapes, and spatial relationships.
• Real-World Connections : Applying number sense to everyday situations like money, time, measurement, and data.

These components foster a solid foundation in number sense, enhancing a child’s mathematical understanding and problem-solving abilities.

Why Is Number Sense Important?

• Number sense forms a crucial foundation for future math mastery. Understanding number sense helps individuals manage personal finances, such as budgeting and understanding interest rates on loans.
• Strong number sense improves understanding and confidence in working with numbers. Having number sense enables individuals to make informed decisions when comparing prices at the grocery store or calculating discounts during shopping. 
• Children with strong number sense can manipulate numbers and employ flexible problem-solving strategies. Being able to estimate tips at a restaurant or mentally calculate sale prices during shopping showcases the practical application of number sense.
• Number sense allows individuals to recognize patterns and connections in numbers, enhancing problem-solving skills. Analyzing trends in data, such as tracking monthly expenses or understanding population growth, requires strong number sense.
• Poor number sense leads to dependence on fixed procedures and inefficient computation methods. Struggling to calculate sale prices or discounts accurately can be a consequence of weak number sense.
• Developing number sense equips individuals with critical thinking and logical reasoning skills applicable in various academic disciplines and everyday life.Interpreting statistical information in news reports or understanding measurements in recipes require number sense skills.

We now understand the value of number sense and the effect it can have on the young students in our classrooms. I firmly think that a student can benefit from having a solid grasp of numbers in every area of mathematics. Early focus on number sense builds a solid foundation for later grades when it comes to math and problem-solving that is more complex. Thus, it’s necessary to teach number sense at an early age. 

You can teach number sense in the following way:

1. Concentrating on base 

The foundation or base is very important while teaching any concept. Give it some time. Before moving on, make sure students are familiar with each idea. Having a strong understanding of place value and how the number system works from the very beginning will help students as they progress through their learning journey in math.

2. Clear Teaching

Each skill must be explicitly taught in a logical sequence. A critical error we can make is assuming a student understands a concept from years ago. The best opportunity to support students in making connections between concepts and ideas is during explicit teaching. It can be done in a variety of ways, such as whole-class teaching and modeling, facilitated groups, small-group work, or one-on-one interaction.

3. Practical Experience

Children learn by using concrete materials. They also enjoy hands-on activities and games – and enjoyment promotes the best kind of learning. It keeps them intrigued and focused and they learn better compared to just board writing and explanations.

4. Review and Revise!

Start with a week devoted to number skills at the beginning of EVERY SINGLE TERM. It aids in concept reinforcement, prepares students for the term, and also enables them to take up new abilities, concepts, and ideas that they might not have been prepared for in the past. Another method to keep reviewing your number concepts and engage your students’ minds is through your daily math warm up.

Facts on Number Sense

• Number sense refers to a child’s fluidity and flexibility with numbers.
• Children gradually and at varying rates acquire number sense through exploration, visualizing numbers in various contexts, and connecting them in ways that aren’t limited by formal written methods.
• Children who have a strong sense of numbers enjoy exploring and playing with numbers and their connections.
• A strong sense of numbers can be developed by seeing numbers in various situations, recognising patterns, and identifying relationships between numbers.
• Number sense is a key component to building a solid foundation for mathematical understanding.

In this article, we learned what number sense is and how it is necessary to have a good number sense. Children benefit from this by better comprehending the meaning of numbers, developing their mental math skills, and gaining the ability to make connections between numbers and arithmetic in the real world. Now let’s solve some examples and practice problems.

Example 1: Amy is comparing prices at a grocery store to find the best deal. What number sense skill will this activity help Amy? Give some examples of comparing numbers.

Solution:  

This activity will help Amy develop her skill of comparing and understanding numerical values, allowing them to make informed decisions based on prices.

We compare numbers using the symbols >, < , or =.

• 100 < 102
• 545 < 554
• 124  > 121

Example 2: Suppose that you are planning a party and deciding the number of snacks needed for the guests. What number sense skills do you need?

To plan a party and the snacks, you need to estimate the number of guests and the appropriate amount of snacks required. You need the math skill of estimation to make reasonable guesses about quantities and plan accordingly.

Example 3: How does solving a math puzzle involving number patterns help children?

Solving a math puzzle with number patterns involves recognizing and analyzing number patterns. It enhances their ability to identify relationships and predict future numbers.

Example 4: Give a real life example where you use number sense?

Measuring ingredients while following a recipe is a great day-to-day example that requires number sense. This activity will help a child develop their skill of measurement and understanding quantities, enabling them to accurately measure ingredients and follow the recipe’s instructions.

Number Sense in Math - Definition, Examples, Facts

Attend this quiz & Test your knowledge.

Which number sense skill involves understanding the concept of more or less?

An item costs $\$9.5$, but anna assumed it to be $\$10$ for finding the approximate price of 7 suchitems. which skill did she use, write the correct number for the following. 2000 + 200 + 20 + 4.

At what age do kids learn numbers and start counting ?

Children develop the ability to understand the actual concept of counting generally around the ages of two and four. By the age of four, children usually can count up to 10 and/or beyond.

What is subitising?

Subitising is instantly recognizing the number of objects in a small group, without counting. For example: knowing there are 5 coins here (without counting them).

How and when does number sense begin?

An intuitive sense of number begins at a very early age. Children as young as two years of age can confidently identify one, two or three objects before they can actually count with understanding (Gelman & Gellistel, 1978) But they understand the actual concept of counting generally around the ages of two and four.

Can 2 year olds recognize numbers?

By age 2, a child can count to two (“one, two”), and by 3, he can count to three, but if he can make it all the way up to 10, he’s probably reciting from rote memory. Kids this age don’t yet actually understand, and can’t identify, the quantities they’re naming.

Is number sense a skill?

Number sense refers to a group of skills. It can be learned or improved upon with time, practice, and determination.

What does number sense mean? What are examples of number sense fluency?

Understanding numbers and how they interact is known as having number sense. Children in the primary grades, for instance, learn how to separate and combine numbers when they experiment with and develop fluency with ideas like how to make 10 and how to break up 12 into 10 and 2.

RELATED POSTS

• Reflexive Relation: Definition, Formula, Examples, FAQs
• Zero Slope – Definition, Types, Graph, Equation, Examples
• Word form – Definition with Examples
• Convert Percent to Fraction –  Definition, Steps, Examples
• Radicand: Definition, Symbol, Examples, FAQs, Practice Problems

Math & ELA | PreK To Grade 5

Kids see fun., you see real learning outcomes..

Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever.

Parents, Try for Free Teachers, Use for Free

• Math Article

Number System Questions

Number systems questions are provided here with solutions. In Class 9, we will come across the Number System chapter where we learn the basics of different types of numbers and their applications. In number theory , you may have learned about the different classifications of numbers, such as whole and natural numbers, even and odd numbers, etc. Here, we will solve the problems based on rational and irrational numbers. Students can practice the questions and it would be helpful for the students to understand this chapter. Here, we have provided a variety of number system questions and some important questions for practice. Let us learn in brief about each concept covered in this chapter before we solve a question based on it.

Also, read: Number System For Class 9

Number System Questions with Solutions

1. What are the five rational numbers between 1 and 2?

Solution: We need to find 5 rational numbers between 1 and 2

Divide and multiply both the numbers by (5+1)

6/6 and 12/6 are rational numbers now.

Therefore, the required rational numbers between 1 and 2 are:

6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6.

2. Can we locate √3 on the number line?

Solution: Yes, we can locate it.

Follow the steps to locate it: Construct BD of unit length perpendicular to OB

Then using the Pythagoras theorem, we see that OD = √((√2) 2 +1 2 ) = √3

With centre O and radius OD, using a compass, draw an arc that cuts the number line at the point Q.

4. Show that 0.3333…, can be expressed in the form of rational number, i.e. p/q.

Solution: Let x = 0.33333

10 x = 10 × (0.333…) = 3.333…

We can write,

3.3333… = 3 + 0.3333… = 3 + x

10 x = 3 + x

5. Write the following in decimal form and mention what expansion it is.

(i) 36/100 = 0.36

It is terminating.

(ii) 1/11 = 0.09090909…

It is non-terminating and repeating

6. Add 2√2 + 5√3 and √2 – 3√3.

Solution: (2√2 + 5√3) + (√2 – 3√3)

= (2+1)√2+(5-3)√3

7. Multiply 6√2 by 2√2.

Solution: 6√2 x 2√2

6 x 2 x √2 x √2

8. Rationalise the denominator of 1/√3

Solution: To rationalise the denominator of 1/√3, we need to multiply the numerator and denominator by √3

1/√3 x (√3/√3) = √3/3

9. Rationalise the denominator of √2/(√3-√5).

Solution: Multiply both numerator and denominator by √3+√5

Numerator = √2(√3+√5)

Denominator = (√3-√5)(√3+√5) = (√3) 2 -(√5) 2 = 3-5 = -2

= [-√2(√3+√5)]/2

10. Simplify:

(i) 2 1/3 .2 2/3

(ii) (3 1/5 ) 4

(iii) 7 1/3 /7 1/5

(iv) 13 1/7 .17 1/7

(iii) (7 1/3 )/(7 1/5 )

= 7 ( 1/3)-(1/5)

= (13.17) 1/7

Video Lesson

Number system and factorisation.

Number System Questions for Practice

• If (p ×q) = 6p-4q+3pq, then find the value of [(6×3)+(4×3)]
• Find out which of the following numbers are prime numbers, given that “p” is a prime number.

(a) 2p  (b)p 2 (c)3p (d) p-2 (e) p-3

• Write down the five rational numbers between 6/5 and 7/5
• Express the decimal number 1.2343 in the form of a rational number (i.e p/q form)
• Simplify the expression (2 2 -3)x. (4+2 2 )

Frequently Asked Question on the Number System Questions

What is meant by number system.

In mathematics, a number system is defined as the way of expressing numbers. The number system provides a distinct way of expressing different types of numbers and it also provides the algebraic structure of the mathematical problem.

What are the different types of numbers?

The different types of numbers are: Natural Numbers Whole numbers Real Numbers Rational Numbers Irrational numbers Complex numbers

Why do we use numbers?

The numbers are used to count the surrounding thing. Numbers are used for expressing money, time, date, and so on. Without numbers, we could not be able to understand the value of many things

What are the four different types of number systems?

The four major types of number system are: Binary number system (base 2 number system) Octal number system (base 8 number system) Decimal number system (base 10 number system) Hexadecimal number system (base 16 number system)

What are the applications of the number system?

The most common application of the number system is found in computer technology. It uses the binary number system. The base 2 number system is used in the process of digital encoding

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Very nice questions with explaintion

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

What is number sense?

By Bob Cunningham, EdM

At a glance

Number sense refers to a group of key math abilities.

It includes the ability to understand quantities and concepts like more and less .

Some people have stronger number sense than others.

Number sense is a group of skills that allow people to work with numbers. These skills are key to doing math — and many other tasks.

Number sense involves:

Understanding quantities

Grasping concepts like more and less , and larger and smaller

Understanding the order of numbers in a list: 1st, 2nd, 3rd, etc.

Understanding symbols that represent quantities ( 7 means the same thing as seven )

Making number comparisons (12 is greater than 10)

Recognizing relationships between single items and groups of items ( seven means one group of seven items)

Some people have stronger number sense than others. Kids and adults with poor number sense may struggle with basic math operations like addition and multiplication. They can also have trouble with everyday tasks and skills like measuring, handling money, and judging time.

Trouble with number sense often shows up early, as kids learn math. For some people, the difficulty lasts into adulthood. But with time and practice, these skills can improve.

Dive deeper

Examples of trouble with number sense.

Here are examples of what it looks like when people struggle with number sense.

Adding and subtracting. Imagine a pile of seven beads. Then take away two of them. People with poor number sense might not realize that:

The number of beads has shrunk

Subtracting the two beads means the group of seven is now a group of five 

Now imagine adding three beads to the pile. If someone struggles with number sense, they might not recognize that:

The group of beads has gotten larger

Adding three beads to the pile of seven makes it a pile of 10

Multiplying and dividing. When people need to combine items from several groups, they might go through the trouble of adding them. They may not grasp that it’s simpler to multiply them.

Likewise, they might not recognize that division is the simplest way to break up groups into their component parts.

Not grasping these concepts makes learning math and using it in everyday life a challenge. Learn more about math challenges in kids .

How schools can help

When kids struggle with math, schools often focus first on reteaching the specific math skills being taught in class. But this approach often doesn’t work for kids who struggle with number sense.

In that case, schools usually turn to an intervention process, where kids typically:

Work with “manipulatives” like blocks and rods to understand the relationships between amounts

Do exercises that involve matching number symbols to quantities

Get a lot of practice estimating

Learn strategies for checking an answer to see whether it’s reasonable

Talk with their teacher about the strategies they use to solve problems

Get help correcting mistakes they make along the way

For many kids with weak number sense, intervention is enough to catch up. But some kids need more support. They may need to be evaluated for special education to get the help they need.

Learn about intervention systems like RTI or MTSS .

How parents and caregivers can help

It takes time for kids to build number sense skills. But there are many ways to help. Here are some examples:

Practice counting and grouping objects. Then add to, subtract from, or divide the groups into smaller groups to practice operations. Combine groups to show multiplication. 

Work on estimating. Build questions into everyday conversations, using phrases like “about how many” or “about how much.”

Talk about relationships between quantities. Ask kids to use words like more and less to compare things.

Build in opportunities to talk about time. Ask kids to keep track of how long it takes to drive or walk to the grocery store. Compare that with how long it takes to get to school. Ask which takes longer.

Learn more strategies to help kids with math .

Explore related topics

Talk to our experts

1800-120-456-456

• Number System Questions

Solved Examples of the Number System along with the Practice Questions

Number System is one of the most important topics of the Maths subject which the students are required to master. And the best way to master the chapter on the number system is by practicing the questions from the said chapter. But along with the practice students do need the solution of the same so that they can be sure about their progress. Hence Vedantu provides to all the students the practice questions of the number system, as well as solved examples of the same so that before attempting the practise questions students can see the examples and have a mental preparation

An Overview of the Number System

Before going directly into the practice questions of the number system, let us first have a brief understanding of the number system, and revise the concepts of it, so that you find it easy to solve the practice questions.

A method of expressing the numbers on the number line, using numerical symbols, is known as Number System. As you can see there are two terms in particular in this definition to understand in a better manner, which are:

Number Line: it is a straight line that real numbers at a fixed interval. All the types of numbers are included in the number line, that is to say, natural numbers, rational numbers, integers etc.

Numerical Symbols: it simply means the mathematical digits, that represents the numbers, which are from 0 to 9.

An Overview of Different Types of Numbers

All the types of numbers are represented in the number line and hence they are all part of the number system, therefore, let us have a quick review of all the types of numbers.

Natural Number: These are the numbers that we use in our day-to-day life because it is widely used in counting, therefore natural numbers are also called counting numbers. It includes all the positive numbers which are not a fraction, and also, it does not include 0. The range of the natural number is 1 to infinity.

Whole Numbers: Add zero to the natural number and you have the whole numbers , that is to say, it includes all the natural numbers and also the 0. Therefore, from 0 to infinity all the numbers are whole numbers.

Integers: It includes all the whole numbers, along with the negative numbers, that is to say, -1, -2, -3. But it does not include the fractions. From the negative infinity number to the positive number in infinity, are all Integers.

Fractions: The numbers which are written in the form of, where b is always a natural number.

Rational Numbers: These numbers can also be represented in fractional form, the difference between rational numbers and fractions is that rational numbers can be any integers except for the 0 as the denominator.

Irrational Numbers: These are the numbers that cannot be represented in a fractional manner such as the root of 2 (\[\sqrt{2}\]) and pie (π)

Real Numbers: When we combine the whole numbers, integers, and fractions are all real numbers. In a simple manner, all the integers along with the decimals and fractions are real numbers.

Prime Numbers: The numbers which only have two factors, which are 1 and the number itself are called prime numbers. For example, 37, can only be divided by 1 and by 37 itself.

The Number System is an important chapter of mathematics. A student needs to be strong in the fundamentals of the number system to solve other problems related to Maths. Some students face difficulty in solving sums of the number system. So, here in this article, we have provided some crucial sums relating to the number system. A student can practice these questions, and it would be easy for him/her to understand the chapter. In this article, we have provided various questions based on number systems such as number system questions and answers, number system practice questions, MCQs on number systems and many other important questions.

Number System Questions and Answers

1. Determine whether the numbers are rational or irrational.

\[ \sqrt{2}\]

\[\sqrt{100}\]

Ans: A rational number is a number that can be represented in the form of p/q, whereas an irrational number cannot be represented in the form of p/q. So,

\[ \sqrt{2}\] is Irrational.

1.5 is Rational.

\[\sqrt{100}\] is Rational.

3.14 is Irrational.

2. Without Actual Division, a state which of the following is a terminating decimal.

\[\frac{9}{25}\]

\[ \frac{37}{78}\]

Ans: In \[\frac{9}{25}\], the prime factors of denominator 25 are 5,5. Thus, it is a terminating decimal. 

In \[ \frac{37}{78}\], the prime factors of denominator 78 are 2, 3, and 13. Thus, it is a non-terminating decimal.

3. Express each of the following as a rational number in the form of p/q, where q ≠ 0.

\[\overline{0.6}\]

\[ \overline{0.43}\]

Ans:   1. Let x = 0.6666 …..(i)

Multiplying both side of eqn (i) by 10 we get,

10x = 6.6666…..(ii)

Now, subtracting eqn (i) from eqn (ii) we get, 

10x = 6.6666

⇒ x = 6/9 which is equal to ⅔, So the required fraction is ⅔.

2. Let x = 0.43434343….(i)

Multiplying both sides of eqn (i) by 100 we get,

100x = 43.43434343…..(ii)

Now, subtracting eqn (i) from eqn (ii) we get,

100x = 43.43434343

x = 0.43434343

⇒ x = \[\frac{43}{99}\], Hence the fraction is \[\frac{43}{99}\].

4. Find 4 rational numbers between 1 and 2.

Ans: To find 4 rational numbers between 1 and 2, we need to divide and multiply both the numbers by (4 + 1) which is 5. So we get,

\[1 \times \frac{5}{5} = \frac{5}{5}\] and \[ 2 \times \frac{5}{5}\] = \[\frac{10}{5}\], Therefore the rational numbers are:

\[\frac{5}{5}\], \[\frac{6}{5}\], \[\frac{7}{5}\], \[\frac{8}{5}\], \[\frac{9}{5}\], \[\frac{10}{5}\].

5. Compare the following numbers.

(i) 0 and \[-\frac{9}{5}\].

(ii) \[-\frac{17}{20}\] and \[-\frac{13}{20}\].

(iii) \[\frac{40}{29}\] and \[\frac{141}{29}\].

Ans: (i) We know that a negative number is always less than 0. Therefore,

0 > - \[\frac{9}{5}\].

(ii) Here the denominator is the same and we know that -17 < -13. Therefore, 

\[\frac{-17}{20}\] < \[\frac{-13}{20}\].

(iii) Here the denominator is the same and we know that 40 < 141. Therefore,

\[\frac{40}{29}\] < \[\frac{141}{29}\].

6. Write the following in decimal numbers and state what expansion it is.

(i) \[\frac{40}{100}\]  (ii) \[\frac{9}{10}\]  (iii) \[\frac{9}{37}\] (iv) \[\frac{103}{5}\]

Ans: (i) \[\frac{40}{100}\] is 0.40, and it is terminating.

(ii) \[\frac{9}{10}\] is 0.9, and it is ending.

(iii) \[\frac{9}{37}\] is 0.243243… it is non-terminating.

(iv) \[\frac{103}{5}\] is 20.6, and it is terminating.

7. Insert one rational number between 3/5 and 7/9.

Ans:   If a and b are two rational numbers, then one rational number between these two will be \[\frac{a + b}{2}\]. Hence the required rational number will be 

\[\frac{1}{2} (\frac{3}{5} + \frac{7}{9}) = \frac{1}{2} (\frac{27 + 35}{45}) = \frac{1}{2} \times \frac{62}{45} = \frac{31}{45}\]

So, the rational number is \[\frac{31}{45}\].

Questions on Number System Conversion

Here, we have provided some number system math questions which are based on number system conversion. 

1. Convert each of the following into a decimal number.

(i) \[\frac{4}{15}\]

(ii) \[2\frac{5}{12}\]

(iii) \[\frac{9}{27}\]

(iv) \[5\frac{31}{55}\]

2. Convert the following into a rational number.

(i) \[0.\overline{227}\]

(ii) \[0.\overline{2104}\]

Number System Practice Questions

As we know, practice makes everyone perfect, so for the better understanding of students, we have provided some number system important questions for practice.

1. Show the number √5 on the number line.

\[\sqrt{2}\]

\[ \sqrt{100}\]

Ans: A rational number is a number which can be represented in the form of p/q, whereas an irrational number cannot be represented in the form of p/q. So,

\[\sqrt{2}\] is Irrational.

2. Insert three rational numbers between 4 and 5.

\[ \frac{37}{78} \]

Ans: In \[ \frac{9}{25}\], the prime factors of denominator 25 are 5,5. Thus, it is a terminating decimal. 

In \[\frac{37}{78} \], the prime factors of denominator 78 are 2, 3, and 13. Thus, it is a non-terminating decimal.

3. Represent the following rational numbers in decimal form

(i) \[\frac{18}{42}\]    (ii) \[-\frac{11}{13}\]

4. Rationalise the denominator of

\[ \frac{1}{3-\sqrt{5}} \]

5. Simplify the following expression (24 - 32)a. ( 5 + 23)

FAQs on Number System Questions

1. Give Some MCQs on the Number System.

Some important MCQs on Number System are:

1. From the following choose Co-prime numbers.

(a) 2, 3 (b) 2, 4 (c) 2, 6 (d) 2, 110

2. On adding \[2\sqrt{3}\] and \[3\sqrt{2}\] we get:

(a) \[5\sqrt{5}\] (b) \[5(\sqrt{3} + \sqrt{2})\] (c) \[ 2\sqrt{3} + 3\sqrt{2}\] (d) None of these

3. A rational number between \[\sqrt{2}\] and \[\sqrt{3}\].

(a) 1.9 (b) \[ \frac{( \sqrt{2}.\sqrt{3} )}{2}\] (c)1.5 (b) 1.8

4. Which of the following is irrational?

(a) \[ \frac{\sqrt{4}}{9} \] (b)\[ \frac{\sqrt{12}}{\sqrt{3}}\] (c) \[\sqrt{5}\] (d) \[\sqrt{81}\] 

5. The Value of (16) 3/4 is equal to:

(a) 2 (b) 4 (c) 8 (d) 16

2. What do you mean by Number System? What are its types?

The number system can be defined as the expression of numbers in a written format. These are a set of symbols and rules used to denote numbers. The number system is used to state how many objects are there in a given set. There are different types of number systems, and here we have mentioned some of the types of number systems for better knowledge of students. The following are the types of number systems:

Real Numbers.

Natural Numbers.

Whole Numbers.

Rational Number system.

Irrational Number system.

Complex Number system.

Binary Number system.

Decimal Number System.

Hexa-Decimal Number System.

Octal-Decimal Number System.