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 number 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

Cubes and Cube Roots (A) Cubes and Cube Roots (A)
Squares and Square Roots (A) Squares and Square Roots (A)
Squares up to 32 Squared (A) Squares up to 32 Squared (A)
Common Factors and Greatest Common Factor (A) Common Factors and Greatest Common Factor (A)
Number Line to 100 Counting by 1 Number Line to 100 Counting by 1
Prime Factor Trees (Range 4 to 48) (A) Prime Factor Trees (Range 4 to 48) (A)
Rounding Numbers to the Nearest 1,000 (U.S. Version) (A) Rounding Numbers to the Nearest 1,000 (U.S. Version) (A)
Exponents in Factor Form (A) Exponents in Factor Form (A)
Converting Between Standard, Expanded and Written Forms to 100,000 (A) Converting Between Standard, Expanded and Written Forms to 100,000 (A)
Finding All Factors of a Number (range 4 to 50) (A) Finding All Factors of a Number (range 4 to 50) (A)

Learning Numbers

Worksheets for learning numbers including poster sized number sets and writing numerals worksheets.

Number 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 (black) Poster sized numbers (Outline) Poster sized numbers (Color)
Writing Numerals and Numbers.

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.

Write Numbers to 20 36pt Write Numbers to 20 60pt 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)

Counting Worksheets

Counting worksheets including charts, number lines, collections and skip counting for students who are learning to count and write down numbers in the correct order.

Skip counting with a car theme.

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 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 Eratosthenes Sieve.

100 Charts (1 to a page).

Regular 100 Chart Left-Handed 100 Chart Blank 100 Chart 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 Partial 100 Chart (About 25% filled out)
100 Charts (4 to a page).

Filled in Hundred Charts Left-Handed Hundred Charts Blank Hundred Charts
120 Charts (1 to a page).

Regular 120 Chart Left-Handed 120 Chart Blank 120 Chart 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 Partial 120 Charts (About 25% filled out)
Backwards or Counting Down 120 Charts (1 to a page).

Regular Backwards 120 Chart Left-Handed Backwards 120 Chart Blank Backwards 120 Chart Backwards 120 Chart with Even Numbers Backwards 120 Chart with Odd Numbers Backwards 120 Chart with Multiples of 3 Backwards 120 Chart with Multiples of 4 Backwards 120 Chart with Multiples of 5 Backwards 120 Chart with Multiples of 6 Backwards 120 Chart with Multiples of 7 Backwards 120 Chart with Multiples of 8 Backwards 120 Chart with Multiples of 9 Backwards 120 Chart with Multiples of 10 Backwards Partial 120 Charts (About 25% filled out)
99 Charts.

One of the issues with 100 charts is that they don't include zero, but 99 charts do!

Ninety-Nine Chart Left-Handed Ninety-Nine Chart Four Ninety-Nine Charts Four Left-Handed Ninety-Nine Charts
Counting animals in patterns.

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 in Rectangular Patterns Counting Animals in Circular Patterns Counting Animals in Linear Patterns Counting Animals in Scattered Formations Counting Animals in Mixed Patterns
Counting using 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
Counting Backwards with Numbers to 120 starting at random numbers.

Counting Backwards with Numbers to 120

Rounding Numbers Worksheets

Rounding numbers to various places worksheets with various sizes of numbers.

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 worksheets that use a comma as a thousands separator.

Rounding to Ten Rounding to a Hundred Rounding to a Thousand Rounding to Ten Thousand Rounding to a Hundred Thousand Rounding to a Million
Rounding numbers worksheets that use a half-space as a thousands separator.

Rounding to Ten Rounding to a Hundred Rounding to a Thousand Rounding to Ten Thousand Rounding to a Hundred Thousand Rounding to a Million
Rounding numbers worksheets that use a point as a thousands separator.

Rounding to Ten Rounding to a Hundred Rounding to a Thousand Rounding to Ten Thousand Rounding to a Hundred Thousand Rounding to a Million

Comparing & Ordering Numbers Worksheets

Comparing numbers worksheets to help students learn about magnitude and quantity.

There are many situations where it is important to know the relative size of one number to another, for example, when it comes to money. Several different number formats are included on the comparing and ordering numbers worksheets for those in the U.S., Canada, and European countries who all use different thousands separators. (Tight) means the numbers to be compared are close to one another.

General comparing numbers worksheets.

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 numbers worksheets that use a comma as a thousands separator.

Comparing Numbers to 10,000 Comparing Numbers to 10,000 (tight) Comparing Numbers to 100,000 Comparing Numbers to 100,000 (tight) Comparing Numbers to 1,000,000 Comparing Numbers to 1,000,000 (tight) Comparing Numbers to 10,000,000 Comparing Numbers to 10,000,000 (tight)
Comparing numbers worksheets that use a half-space as a thousands separator.

Comparing Numbers to 10 000 Comparing Numbers to 10 000 (tight) Comparing Numbers to 100 000 Comparing Numbers to 100 000 (tight) Comparing Numbers to 1 000 000 Comparing Numbers to 1 000 000 (tight) Comparing Numbers to 10 000 000 Comparing Numbers to 10 000 000 (tight)
Comparing numbers worksheets that use a point as a thousands separator.

Comparing Numbers to 10.000 Comparing Numbers to 10.000 (tight) Comparing Numbers to 100.000 Comparing Numbers to 100.000 (tight) Comparing Numbers to 1.000.000 Comparing Numbers to 1.000.000 (tight) Comparing Numbers to 10.000.000 Comparing Numbers to 10.000.000 (tight)
Ordering numbers worksheets.

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

Expanded Form Worksheets

Expanded form worksheets for learning about place value and number concepts.

General expanded form worksheets.

Write Expanded Form (range 100 to 999)
Writing expanded form worksheets that use a comma as a thousands separator.

Write Expanded Form (range 1,000 to 9,999) Write Expanded Form (range 10,000 to 99,999) Write Expanded Form (range 100,000 to 999,999) Write Expanded Form (range 1,000,000 to 9,999,999)
Writing expanded form worksheets that use a half-space as a thousands separator.

Write Expanded Form (range 1 000 to 9 999) Write Expanded Form (range 10 000 to 99 999) Write Expanded Form (range 100 000 to 999 999) Write Expanded Form (range 1 000 000 to 9 999 999)
Writing expanded form worksheets that use a point as a thousands separator.

Write Expanded Form (range 1.000 to 9.999) Write Expanded Form (range 10.000 to 99.999) Write Expanded Form (range 100.000 to 999.999) Write Expanded Form (range 1.000.000 to 9.999.999)

Written Numbers Worksheets

Writing and reading numbers worksheets for students to learn how to write numbers in words and vice-versa.

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.

General writing numbers in words worksheets.

Writing Numbers to 10 Writing Numbers to 50 Writing Two-digit Numbers Writing Three-digit Numbers
Writing numbers in words worksheets that use a comma as a thousands separator.

Writing Four-digit Numbers Writing Five-digit Numbers Writing Six-digit Numbers Writing Seven-digit Numbers Writing Eight-digit Numbers Writing Nine-digit Numbers
Writing numbers in words worksheets that use a half-space as a thousands separator.

Writing Four-digit Numbers Writing Five-digit Numbers Writing Six-digit Numbers Writing Seven-digit Numbers Writing Eight-digit Numbers Writing Nine-digit Numbers
Reading written numbers worksheets.

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 Written Two-Digit Numbers Reading Written Three-Digit 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
Converting between standard, expanded and written forms.

The standard, expanded and written forms conversion worksheets sum up the previous sections by including all three number forms on the same page.

Numbers to 1000 Numbers to 10,000 Numbers to 100,000 Numbers to 1,000,000 Numbers to 10,000,000

Scientific Notation Worksheets

Scientific notation worksheets for learning how to write and interpret numbers in this format.

Converting Ordinary Numbers to Scientific Numbers.

Large Numbers Only Small Numbers Only Large and Small Numbers
Converting Scientific Numbers to Ordinary Numbers.

Large Numbers Only Small Numbers Only Large and Small Numbers
Converting Between Ordinary Numbers and Scientific Numbers.

Large Numbers Only Small Numbers Only Large and Small Numbers

Roman Numerals Worksheets

Roman numerals worksheets for converting between standard and Roman numerals.

This is about as "old school" as you can get. Put on your tunica 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 between Roman numerals and standard 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 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 up to XXV Adding Roman Numerals up to C Adding Roman Numerals up to M Adding Roman Numerals up to MMMCMXCIX 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 up to C Multiplying Roman Numerals up to M Multiplying Roman Numerals up to MMMCMXCIX Dividing Roman Numerals up to C Dividing Roman Numerals up to M Dividing Roman Numerals up to MMMCMXCIX 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 Worksheets

Factors and factoring worksheets including listing factors of numbers and finding prime factors of numbers using a tree diagram.

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.

Finding all factors of numbers.

All Factors of a Number (range 4 to 50) All Factors of a Number (range 50 to 100) All Factors of a Number (range 100 to 200) All Factors of a Number (range 200 to 400)
Finding prime factors of numbers with factor trees.

Prime Factors Using a Tree Diagram (range 4 to 48) Prime Factors Using a Tree Diagram (range 4 to 96) Prime Factors Using a Tree Diagram (range 4 to 144) Prime Factors Using a Tree Diagram (range 48 to 192) Prime Factors Using a Tree Diagram (range 48 to 240)
Greatest Common Factors.

Greatest Common Factors

Roots and Exponents Worksheets

Roots and exponents worksheets including squares and cubes and writing exponents in factor form.

Squares and square roots.

Squares (up to 32²) Squares (up to 99²) Square Roots (Perfect Squares) Squares and Square Roots (Easier)
Cubes and cube roots.

Cubes Cube Roots Cubes and Cube Roots (Easier than above)
More exponents.

Exponents in Factor Form

Binary and Other Base Number Systems

Binary and other base number systems worksheets for learning about number systems with bases other than 10.

Binary numbers worksheets.

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.

This 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 Place Value Chart Mystery Number Trick
Converting between base number systems worksheets.

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 to Decimal Converting from Binary to Octal Converting from Binary to Hexadecimal Converting from Binary to Various Other Base Sytems 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 to Decimal Converting from Hexadecimal to Binary Converting from Hexadecimal to Octal Converting from Hexadecimal to Various Other Base Sytems 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, 1112 (the 2 stands for binary or base 2) is 78 (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, 1110101010001112 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 725078. If you can express the octal numbers from 0 to 7 in binary, you can easily convert the other way. For example 72238 = 1110100100112 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 43315 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: 15037.

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 37508 to hexadecimal (base 16). 16 in base 8 is 208. The first step is to divide 37508 by 208 = 1768 R 108. Next, divide 1768 by 208 to get 78 R 168. Finally, 78 divided by 208 is 08 R 78. 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. 78 is 716, 168 is (14 in decimal) E16, and 108 is 816. So, the number 37508 is 7A816.