counting in powers of 10 problem solving

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:

Interpret fractions as decimals

Powers of 10

Here you will learn about powers of 10, including what they are and how to write and solve equations using powers of 10.

Students will first learn about powers of 10 as part of numbers and operations in base ten in 5th grade.

What are powers of 10?

Powers of \bf{10} are 10 multiplied by itself over and over again and written with exponents.

For example,

Since our number system is Base 10 (meaning each place value position is grouped by tens), when numbers are multiplied or divided by powers of 10, place value patterns are created.

\begin{aligned} & 67 \times 10=670 \\\\ & 67 \times 10^2=6,700 \\\\ & 67 \times 10^3=67,000 \end{aligned}

The digits from the original number (67) are always in the product, but they increase in place value.

Notice that each time an additional 10 is multiplied, the number of place value positions the digits move increases by one.

This is also true when dividing with powers of 10.

\begin{aligned} & 67 \div 10=6.7 \\\\ & 67 \div 10^2=0.67 \\\\ & 67 \div 10^3=0.067 \end{aligned}

The digits for the original number (67) are always in the quotient, but they decrease in place value.

Notice that each time an additional 10 is divided, the number of places the digits move increases by one.

Common Core State Standards

How does this relate to 5th and 6th grade math?

• Grade 5 – Numbers and Operations in Base Ten (5.NBT.2) Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number powers of 10 to denote powers of 10.

How to use powers of 10

In order to represent a number as a power of 10 :

Show the number as an expression with multipliers of \bf{10} .

Count the number of \bf{10} s in the expression to create the power of \bf{10} .

Write the equation.

In order to solve an expression with a power of 10 :

Use place value reasoning to identify how the power of \bf{10} will change the number.

Shift the digits left if multiplying and shift the digits right if dividing.

[FREE] Exponents Check for Understanding Quiz (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of exponents. 15+ questions with answers covering a range of 5th and 6th grade exponents topics to identify areas of strength and support!

Powers of 10 examples

Example 1: number as a power of 10.

Write 45,000 as a power of 10.

45,000 is the same as 45 thousands or 45 \times 1,000.

1,000 as a product of tens is 10 \times 10 \times 10, so…

45,000=45 \times 10 \times 10 \times 10

2 Count the number of \bf{10} s in the expression to create the power of \bf{10} .

There are 3 tens being multiplied. Use 10 as the base and 3 as the exponent.

3 Write the equation.

45,000=45 \times 10^3

*Note: You can show 45,000 with other powers of 10. See how in the next example.

Example 2: number as multiple powers of 10

Write 1,030,000 as two different powers of 10.

1,030,000 is the same as 103 ten-thousands or 103 \times 10,000.

10,000 as a product of tens is 10 \times 10 \times 10 \times 10, so…

1,030,000=103 \times 10 \times 10 \times 10 \times 10

1,030,000 is also the same as 1,030 thousands or 1,030 \times 1,000.

1,030,000=1,030 \times 10 \times 10 \times 10

There are 4 tens being multiplied. Use 10 as the base and 4 as the exponent.

1,030,000=103 \times 10^4

1,030,000=1,030 \times 10^3

*Note: The example shows two possible powers of 10 equations, but any place value can be used to show powers of 10.

Example 3: expression with a power of 10 – product

Solve 5.3 \times 10^6 using place value reasoning.

10^6=10 \times 10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times larger than the position to the right, 5.3 will be 6 place value positions larger after it is multiplied by 10^6.

Multiplying by 10, makes a number 10 times larger, which shifts the digits to the left.

For \times 10^6, shift the digits 6 positions to the left.

Example 4: expression with a power of 10 – quotient

Solve 80,800,000 \div 10^7 using place value reasoning.

10^7=10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 80,800,000 will be 7 place value positions smaller after it is divided by 10^7.

Dividing by 10, makes a number 10 times smaller, shifts the digits to the right.

For \div 10^7, shift the digits 7 positions to the right.

Example 5: expression with a power of 10 – missing operation and power of 10

Complete the equation using an operation with a power of 10 :

The 5 in 5.16 is in the ones position.

The 5 in 51,600 is in the ten-thousands position.

From 5.16 to 51,600 the power of 10 changes the number by 4 place value positions.

This means the power of 10 is 10^4.

The place value of the 5, 1 , and 6 grows larger by 4 positions. Because of this, the digits shift to the left and the operation is multiplication.

5.16 \times 10^4=51,600

Example 6: expression with a power of 10 – missing dividend

Complete the equation:

10^8=10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 0.109 is 8 place value positions smaller than the dividend that was divided by 10^8.

The 1, 0 , and 9 in dividend will be 8 place value positions larger than in the quotient, 0.109.

Even though the equation operation is division, to find the quotient, work backwards and shift the digits to the left.

10,900,000 \div 10^8=0.109

Teaching tips for powers of 10

• Throughout teaching this skill, never forget that the main purpose is for students to explain patterns and deepen their understanding of place value. While the rules “moving the decimal point” or “adding zeros” may come up in discussions, students who memorize these rules and never make place value connections will not truly master the standard – even if they can rotely solve these types of problems.
• Worksheets are useful for this skill, but be sure they include a variety of question types. Worksheets that only include solving for the product or quotient and/or do not ask students to explain the place value connection, will promote only a rote understanding of this skill.

Easy mistakes to make

• Not knowing what to do when there are \bf{0} s within (not just at the end) Students are quick to notice a pattern between the power of 10 and the amount of 0 s at the end of many numbers. However, if students only see numbers that have 0 s at the end, they may create solving strategies that don’t work with all numbers. This could cause mistakes when dealing with numbers like 304,000 or expressions like 5.06 \times 10^4. It is important to expose students to these types of numbers and equations from the beginning, to help avoid this misconception.

• Forgetting about an exponent of \bf{1} 10 by itself is technically 10^1. It is not typically written this way, but it is important to remember that the exponent of 1 is there.

Related exponents lessons

• Negative exponents

Practice powers of 10 questions

1. Which expression shows 19,000 as a power of 10?

19,000 is the same as 19 thousands or 19 \times 1,000.

19,000=19 \times 10 \times 10 \times 10

19,000=19 \times 10^3

2. Which expression shows 2,030,000 as a power of 10?

2,300,000 is the same as 2.03 millions or 2.03 \times 1,000,000.

1,000,000 as a product of tens is 10 \times 10 \times 10 \times 10 \times 10 \times 10, so…

2,030,000=2.03 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10

There are 6 tens being multiplied. Use 10 as the base and 6 as the exponent.

2,030,000=2.03 \times 10^6

3. Solve 180 \times 10^5.

10^5=10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times larger than the position to the right, 180 will be 5 place value positions larger after it is multiplied by 10^5.

Multiplying by 10, moves all the digits up one position.

For \times 10^5, shift the digits 5 times to the left.

Notice in this case, since 180 is a whole number, that \times 10^5 also “adds” 5 zeros.

This happens for the same reason the decimal point “moves.”

The place value is growing by 5 positions, so each new position needs a 0 as a place holder.

4. Solve 4,100 \div 10^4.

10^4=10 \times 10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 4,100 will be 4 place value positions smaller after it is divided by 10^4.

Dividing by 10, shifts all the digits down one position.

For \div 10^4, shift the digits 4 times to the right.

5. Which equation is true?

The 4 in 4.6 is in the ones position.

The 4 in 460,000,000 is in the hundred-millions position.

This is a change of 8 place value positions.

This means the power of 10 is 10^8.

The place value of the 4 and 6 grows larger by 8 positions. Because of this, the digits shift to the left and the operation is multiplication.

6. Which number completes the equation?

10^3=10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 702 is 3 place value positions smaller than the dividend that was divided by 10^3.

The 7, 0 , and 2 in dividend will be 3 place value positions larger than in the quotient, 702.

702,000 \div 10^3 = 702

Powers of 10 FAQs

For this standard, powers of 10 are useful in identifying and understanding place value patterns. In later grades, this skill is referred to as scientific notation and is used to represent very small numbers and very large numbers in a more efficient way.

The number of times the decimal place moves is the same as the exponent when 10 is the base. The operation, multiplication or division, tells which direction to move the decimal place.

Yes, although this standard only covers positive powers, in later grades, students will work with negative powers of ten.

Per the Common Core, in 5th grade, students work with the tenth, hundredth, and thousandth positions. However, in real world applications, powers of 10 have no limit as to how many decimal points they can represent. It is common that they include numbers up to billionth or even smaller positions. In fact, one of the purposes of powers of 10 is to make it easier to write very, very small numbers.

Yes, scientific calculators in particular include an exponent function that can be used to input and solve an equation with a power of 10.

The next lessons are

• Algebraic expressions
• Math equations
• Inequalities

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 (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

Privacy Overview

Powers of Ten Worksheets

Welcome to the powers of ten math worksheets page at Math-Drills.com where you have the power to learn this important skill! This page includes Powers of ten math worksheets with whole numbers and decimals in comma/point and point/comma formats for students to learn this important skill.

Understanding how to multiply and divide by powers of ten is one of those essential skills that students can't do without. It makes it easier to use estimation skills, it is essential in learning large and small numbers, and solidifies an understanding of place value and numbers in general. This page includes a lot of powers of ten worksheets with whole numbers on them because there are fewer digits to work with and the decimal place is in a consistent location which means that the whole number worksheets will prove to be a nice stepping stone to the more difficult decimal versions further down the page.

Positive powers of ten refers to 10, 100, and 1,000. Negative powers of ten refers to 0.1, 0.01, and 0.001. We've supplied worksheets in both standard form and exponent form. In case this is new to you, 10 -3 = 0.001, 10 -2 = 0.01, 10 -1 = 0.1, 10 0 = 1, 10 1 = 10, 10 2 = 100, 10 3 = 1000.

Most Popular Powers of Ten Worksheets this Week

Learning Powers of Ten

The learning to multiply by powers of ten worksheets include the same number multiplied by the positive or negative powers of ten. This allows students to see patterns in multiplying or dividing by a set of powers of ten.

A good place to start is with the powers of ten in standard form. Later on, introduce students to the exponent form as they will already know how to multiply or divide with powers of ten and can focus on learning the relationship between the exponents and the number of zeros they need to work with.

• Learning To Multiply Whole Numbers By Powers Of Ten (Standard Form) Numbers from 1 to 10 × Positive Powers of Ten (Standard Form) Two-Digit Numbers × Positive Powers of Ten (Standard Form) Numbers from 1 to 10 × Negative Powers of Ten (Standard Form) Two-Digit Numbers × Negative Powers of Ten (Standard Form) Whole Number × Negative Powers of Ten (Whole Number Results) (Standard Form)
• Learning To Multiply Whole Numbers By Powers Of Ten (Exponent Form) Numbers from 1 to 10 × Positive Powers of Ten ( Exponent Form) Two-Digit Numbers × Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Negative Powers of Ten ( Exponent Form) Two-Digit Numbers × Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Negative Powers of Ten (Whole Number Results) ( Exponent Form)

Multiplying with multiples of powers of ten has tremendous benefits in mental math. Think about long multiplication which is essentially multiplying by multiples of powers of ten. For example, 456 × 4 can be thought of as 4 × 400 + 4 × 50 + 4 × 6. The more comfortable students are with handling all those extra zeros, the less often they will make mistakes.

• Learning To Multiply Whole Numbers By Multiples of Powers Of Ten (Standard Form) Numbers from 1 to 10 × Multiples of Positive Powers of Ten (Standard Form) Two-Digit Numbers × Multiples of Positive Powers of Ten (Standard Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten (Standard Form) Two-Digit Numbers × Multiples of Negative Powers of Ten (Standard Form) Whole Number × Multiples of Negative Powers of Ten (Whole Number Results) (Standard Form)
• Learning To Multiply Whole Numbers By Multiples of Powers Of Ten (Exponent Form) Numbers from 1 to 10 × Multiples of Positive Powers of Ten ( Exponent Form) Two-Digit Numbers × Multiples of Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten ( Exponent Form) Two-Digit Numbers × Multiples of Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten (Whole Number Results) ( Exponent Form)

The learning to divide by powers of ten worksheets include the same number divided by the positive or negative powers of ten.

• Learning To Divide Whole Numbers By Powers Of Ten (Standard Form) Numbers from 1 to 10 ÷ Positive Powers of Ten (Standard Form) Two-Digit Numbers ÷ Positive Powers of Ten (Standard Form) Numbers from 1 to 10 ÷ Negative Powers of Ten (Standard Form) Two-Digit Numbers ÷ Negative Powers of Ten (Standard Form) Whole Number ÷ Positive Powers of Ten (Whole Number Results)
• Learning To Divide Whole Numbers By Powers Of Ten (Exponent Form) Numbers from 1 to 10 ÷ Positive Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Negative Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Positive Powers of Ten (Whole Number Results) ( Exponent Form)
• Learning To Divide Whole Numbers By Multiples of Powers Of Ten (Standard Form) Numbers ÷ Multiples of Positive Powers of Ten (Standard Form) (Quotients 1 to 10 ) Numbers ÷ Multiples of Positive Powers of Ten (Standard Form) (Quotients 10 to 99 ) Numbers ÷ Multiples of Negative Powers of Ten (Standard Form) (Quotients 1 to 10 ) Numbers ÷ Multiples of Negative Powers of Ten (Standard Form) (Quotients 10 to 99 ) Whole Number ÷ Multiples of Positive Powers of Ten (Whole Number Results)
• Learning To Divide Whole Numbers By Multiples of Powers Of Ten (Exponent Form) Numbers from 1 to 10 ÷ Multiples of Positive Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Multiples of Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Multiples of Negative Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Multiples of Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Multiples of Positive Powers of Ten (Whole Number Results) ( Exponent Form)

Multiplying and Dividing Whole Numbers by Powers of Ten

Multiplying by positive powers of ten always makes a number larger in absolute value. Conversely, multiplying by negative powers of ten always makes a number smaller in absolute value. Multiplying by 10 0 is the same as multiplying by 1.

• Multiplying Whole Numbers By Powers Of Ten (Standard Form) Whole Number × All Powers of Ten (Standard Form) Whole Number × All Positive Powers of Ten (Standard Form) Whole Number × All Negative Powers of Ten (Standard Form) Whole Number × 0.001 Whole Number × 0.01 Whole Number × 0.1 Whole Number × 10 Whole Number × 100 Whole Number × 1,000
• Multiplying Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × All Powers of Ten (Exponent Form) Whole Number × All Positive Powers of Ten (Exponent Form) Whole Number × All Negative Powers of Ten (Exponent Form) Whole Number × 10 -3 Whole Number × 10 -2 Whole Number × 10 -1 Whole Number × 10 1 Whole Number × 10 2 Whole Number × 10 3
• European Format Multiplying Whole Numbers By Powers Of Ten (Standard Form) Whole Number × All Powers of Ten (Standard Form) Whole Number × All Positive Powers of Ten (Standard Form) Whole Number × All Negative Powers of Ten (Standard Form) Whole Number × 0,001 Whole Number × 0,01 Whole Number × 0,1 Whole Number × 10 Whole Number × 100 Whole Number × 1.000
• European Format Multiplying Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × All Powers of Ten (Exponent Form) Whole Number × All Positive Powers of Ten (Exponent Form) Whole Number × All Negative Powers of Ten (Exponent Form) Whole Number × 10 -3 Whole Number × 10 -2 Whole Number × 10 -1 Whole Number × 10 1 Whole Number × 10 2 Whole Number × 10 3

Dividing by positive powers of ten always makes a number smaller in absolute value. Conversely, dividing by negative powers of ten always makes a number larger in absolute value. Dividing by 10 0 is the same as dividing by 1.

• Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number ÷ All Powers of Ten (Standard Form) Whole Number ÷ All Positive Powers of Ten (Standard Form) Whole Number ÷ All Negative Powers of Ten (Standard Form) Whole Number ÷ 0.001 Whole Number ÷ 0.01 Whole Number ÷ 0.1 Whole Number ÷ 10 Whole Number ÷ 100 Whole Number ÷ 1,000
• Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number ÷ All Powers of Ten (Exponent Form) Whole Number ÷ All Positive Powers of Ten (Exponent Form) Whole Number ÷ All Negative Powers of Ten (Exponent Form) Whole Number ÷ 10 -3 Whole Number ÷ 10 -2 Whole Number ÷ 10 -1 Whole Number ÷ 10 1 Whole Number ÷ 10 2 Whole Number ÷ 10 3
• European Format Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number : All Powers of Ten (Standard Form) Whole Number : All Positive Powers of Ten (Standard Form) Whole Number : All Negative Powers of Ten (Standard Form) Whole Number : 0,001 Whole Number : 0,01 Whole Number : 0,1 Whole Number : 10 Whole Number : 100 Whole Number : 1.000
• European Format Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number : All Powers of Ten (Exponent Form) Whole Number : All Positive Powers of Ten (Exponent Form) Whole Number : All Negative Powers of Ten (Exponent Form) Whole Number : 10 -3 Whole Number : 10 -2 Whole Number : 10 -1 Whole Number : 10 1 Whole Number : 10 2 Whole Number : 10 3

These math worksheets should help to mix things up a bit. Mixing up operations on a page helps students pay attention to detail and challenges them to access more processes while they complete the questions. The first worksheets below include all of the powers of ten from 0.001 to 1,000.

• Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number × or ÷ All Powers of Ten (Standard Form) Whole Number × or ÷ All Positive Powers of Ten (Standard Form) Whole Number × or ÷ All Negative Powers of Ten (Standard Form) Whole Number × or ÷ 0.001 Whole Number × or ÷ 0.01 Whole Number × or ÷ 0.1 Whole Number × or ÷ 10 Whole Number × or ÷ 100 Whole Number × or ÷ 1,000
• Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × or ÷ All Powers of Ten (Exponent Form) Whole Number × or ÷ All Positive Powers of Ten (Exponent Form) Whole Number × or ÷ All Negative Powers of Ten (Exponent Form) Whole Number × or ÷ 10 -3 Whole Number × or ÷ 10 -2 Whole Number × or ÷ 10 -1 Whole Number × or ÷ 10 1 Whole Number × or ÷ 10 2 Whole Number × or ÷ 10 3
• European Format Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number × or : All Powers of Ten (Standard Form) Whole Number × or : All Positive Powers of Ten (Standard Form) Whole Number × or : All Negative Powers of Ten (Standard Form) Whole Number × or : 0,001 Whole Number × or : 0,01 Whole Number × or : 0,1 Whole Number × or : 10 Whole Number × or : 100 Whole Number × or : 1.000
• European Format Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × or : All Powers of Ten (Exponent Form) Whole Number × or : All Positive Powers of Ten (Exponent Form) Whole Number × or : All Negative Powers of Ten (Exponent Form) Whole Number × or : 10 -3 Whole Number × or : 10 -2 Whole Number × or : 10 -1 Whole Number × or : 10 1 Whole Number × or : 10 2 Whole Number × or : 10 3

Multiplying and Dividing Decimals by Powers of Ten

Unlike the whole number worksheets above, these worksheets and the dividing and mixed versions that follow include more digits, more need to know place value and consequently, more of a challenge. This is probably not a good place to start if your students are just learning how to multiply and divide by powers of ten. Instead, try the whole number worksheets further up the page. If they are ready, these worksheets should prove to be a fine challenge and will go a long way in helping your students to be successful in their mathematics learning.

• Multiplying Decimal Numbers By Powers Of Ten (Standard Form) Decimal × All Powers of Ten (Standard Form) Decimal × All Positive Powers of Ten (Standard Form) Decimal × All Negative Powers of Ten (Standard Form) Decimal × 0.001 Decimal × 0.01 Decimal × 0.1 Decimal × 10 Decimal × 100 Decimal × 1,000
• Multiplying Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × All Powers of Ten (Exponent Form) Decimal × All Positive Powers of Ten (Exponent Form) Decimal × All Negative Powers of Ten (Exponent Form) Decimal × 10 -3 Decimal × 10 -2 Decimal × 10 -1 Decimal × 10 1 Decimal × 10 2 Decimal × 10 3
• European Format Multiplying Decimal Numbers By Powers Of Ten (Standard Form) Decimal × All Powers of Ten (Standard Form) Decimal × All Positive Powers of Ten (Standard Form) Decimal × All Negative Powers of Ten (Standard Form) Decimal × 0,001 Decimal × 0,01 Decimal × 0,1 Decimal × 10 Decimal × 100 Decimal × 1.000
• European Format Multiplying Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × All Powers of Ten (Exponent Form) Decimal × All Positive Powers of Ten (Exponent Form) Decimal × All Negative Powers of Ten (Exponent Form) Decimal × 10 -3 Decimal × 10 -2 Decimal × 10 -1 Decimal × 10 1 Decimal × 10 2 Decimal × 10 3

It sometimes takes a little time for students to wrap their heads around dividing by powers of ten, especially by negative powers of ten. This is because students are usually taught that dividing makes a number smaller, but when dividing by negative powers of ten, the result is a larger number. Of course, this only applies to numbers that were positive to begin with....

• Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal ÷ All Powers of Ten (Standard Form) Decimal ÷ All Positive Powers of Ten (Standard Form) Decimal ÷ All Negative Powers of Ten (Standard Form) Decimal ÷ 0.001 Decimal ÷ 0.01 Decimal ÷ 0.1 Decimal ÷ 10 Decimal ÷ 100 Decimal ÷ 1,000
• Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal ÷ All Powers of Ten (Exponent Form) Decimal ÷ All Positive Powers of Ten (Exponent Form) Decimal ÷ All Negative Powers of Ten (Exponent Form) Decimal ÷ 10 -3 Decimal ÷ 10 -2 Decimal ÷ 10 -1 Decimal ÷ 10 1 Decimal ÷ 10 2 Decimal ÷ 10 3
• European Format Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal : All Powers of Ten (Standard Form) Decimal : All Positive Powers of Ten (Standard Form) Decimal : All Negative Powers of Ten (Standard Form) Decimal : 0,001 Decimal : 0,01 Decimal : 0,1 Decimal : 10 Decimal : 100 Decimal : 1.000
• European Format Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal : All Powers of Ten (Exponent Form) Decimal : All Positive Powers of Ten (Exponent Form) Decimal : All Negative Powers of Ten (Exponent Form) Decimal : 10 -3 Decimal : 10 -2 Decimal : 10 -1 Decimal : 10 1 Decimal : 10 2 Decimal : 10 3
• Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal × or ÷ All Powers of Ten (Standard Form) Decimal × or ÷ All Positive Powers of Ten (Standard Form) Decimal × or ÷ All Negative Powers of Ten (Standard Form) Decimal × or ÷ 0.001 Decimal × or ÷ 0.01 Decimal × or ÷ 0.1 Decimal × or ÷ 10 Decimal × or ÷ 100 Decimal × or ÷ 1,000
• Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × or ÷ All Powers of Ten (Exponent Form) Decimal × or ÷ All Positive Powers of Ten (Exponent Form) Decimal × or ÷ All Negative Powers of Ten (Exponent Form) Decimal × or ÷ 10 -3 Decimal × or ÷ 10 -2 Decimal × or ÷ 10 -1 Decimal × or ÷ 10 1 Decimal × or ÷ 10 2 Decimal × or ÷ 10 3
• European Format Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal × or : All Powers of Ten (Standard Form) Decimal × or : All Positive Powers of Ten (Standard Form) Decimal × or : All Negative Powers of Ten (Standard Form) Decimal × or : 0,001 Decimal × or : 0,01 Decimal × or : 0,1 Decimal × or : 10 Decimal × or : 100 Decimal × or : 1.000
• European Format Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × or : All Powers of Ten (Exponent Form) Decimal × or : All Positive Powers of Ten (Exponent Form) Decimal × or : All Negative Powers of Ten (Exponent Form) Decimal × or : 10 -3 Decimal × or : 10 -2 Decimal × or : 10 -1 Decimal × or : 10 1 Decimal × or : 10 2 Decimal × or : 10 3

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.

Powers of 10

• Switch to Parent
• Switch to Student

You've reached your daily practice limit of 12 questions.

When you sign up for a free account and login, you can play all you'd like.

(Must be 18 years old to sign up.)

Understanding Powers of 10 in Fifth Grade Math

In fifth grade math, students encounter the concept of Powers of 10, which involves understanding the exponential notation where 10 is multiplied by itself a certain number of times. This concept plays a crucial role in understanding place value, scientific notation, and operations with very large or very small numbers. Powers of 10 provide a systematic way to represent numbers and help students comprehend the magnitude of quantities across various contexts. Mastery of Powers of 10 lays a strong foundation for more advanced mathematical concepts and real-world applications, making it an essential skill for 5th-grade students to develop.

Teaching Strategies for Powers of 10 in the Classroom

Educators utilize various strategies to teach Powers of 10 effectively in the 5th-grade classroom. Interactive lessons that incorporate visual aids, such as place value charts or manipulatives, help students visualize the concept of exponential notation. Engaging activities, such as Powers of 10 games or interactive worksheets, provide opportunities for hands-on practice and reinforce learning. Additionally, incorporating real-world examples and problem-solving tasks into lessons helps students understand the practical applications of Powers of 10. By providing a mix of interactive, hands-on, and real-world learning experiences, educators ensure that students develop a solid understanding of Powers of 10.

Practicing Powers of 10 with iKnowIt.com

iKnowIt.com offers an online platform for fifth-grade students to practice and reinforce their understanding of Powers of 10 in an engaging and interactive way. Through interactive games and exercises, students can explore the concept of Powers of 10 and strengthen their skills. The platform provides a variety of activities designed to cater to different learning styles and abilities, such as Powers of 10 quizzes and interactive lessons. With immediate feedback and progress tracking features, students can monitor their performance and track their improvement over time. iKnowIt.com's interactive approach to learning ensures that students develop a solid foundation in Powers of 10 while having fun.

This interactive math lesson is categorized as Level E. It may be best suited for fifth grade students.

Common Core Standard

5.NBT.2, MA.6.NSO.3.4, 5.4A Number And Operations In Base Ten Understand The Place Value System. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

You might also be interested in...

Equivalent Fractions (Level D) Learn how to determine if fractions are equal or not equal in this lesson.

Exponents (Level E) Learn about exponents and why they are useful in this math lesson.

• Full Site Index
• Membership Info
• School License Info
• Standards ( CC , FL , TX )
• Testimonials
• Monthly Contest
• Training for Teachers
• Roster Setup Service
• Privacy Policy
• Terms of Service

Enter your new class code.

Use only letters, numbers or a dash. The code can not begin with a dash (-)

This field is required and can not be blank.

Enter your class code.

Visual maths worksheets, each maths worksheet is differentiated and visual.

Powers of Ten Problem Solving worksheet

Total reviews: (0), powers of ten problem solving worksheet description.

Perfect to use after a series of lessons on powers of ten and standard form, this worksheet provides some problem-solving activities for learners to apply their skills.

Section A features a completion table involving decimal numbers and numbers in standard form.

Section B then provides a worded problem involving ratios of scale and volume.

Section C then has another worded problem again involving a ratio.

Related to Powers of Ten Problem Solving worksheet:

We love to get your feedback:, get 20 free maths worksheets.

Fill out the form below to get 20 FREE maths worksheets!

Count in Powers of 10

If you are counting in 10s, the tens place changes. If you are counting in 100s, the hundreds place changes. If you are counting in 1000s, the thousands place changes. If you are counting in 10000s, the ten thousands place changes. 

Now try a few practice questions!

Welcome to DoodleMaths!

Ready to try some questions?  Download the DoodleMaths app to practice questions for free today!

Try DoodleMaths for free!

What we offer

Quick links

All rights reserved. 

Are you a parent, teacher or student?

Get started for free!

Maths information pack

We ask for your contact info so we can send our info pack directly to your inbox for your convenience, exam prep information pack, case studies information pack.

Book a chat with our team

I’m new to Doodle

My school is already using Doodle

Information pack

We ask for your contact info so that our education consultants can get in touch with you and let you know a bit more about doodle., student login, which programme would you like to use.

DoodleMaths

DoodleTables

DoodleEnglish

DoodleSpell

If you’d like to use Doodle’s browser version, please visit this page on a desktop.

To log in to Doodle on this device, you can do so through our apps. You can find out how to download them here:

Powers of 10

By the end of this unit, students will be able to:

• Understand the concept of powers of 10 and their relationship to place value.
• Count forward and backward in powers of 10.
• Recognize the pattern of multiplying by 10 to move between place value positions.
• Apply the concept of counting in powers of 10 to solve real-life and mathematical problems.

What's Included

• Three-part Lesson
• Self-marking Activities
• Fluency, Reasoning and Problem-solving Questions.
• Engaging Drag and Drop Activities
• Interactive Self-marking Worksheet
• Printable Worksheets to Consolidate Learning

Year 2 Mathematics:

Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations, and arrays.

• England & Wales: Year 5
• Scotland: Primary 5
• Rep. Ireland: Fourth Class
• Australia: Grade 4
• USA: Grade 4

Connected Resources

Rounding to One Decimal Place

Comparing and Ordering Numbers to 100000

Place Value

Rounding Numbers to the Nearest 10, 100…

Hear from other teachers.

Ok, I get the point!

Get unlimited access to the entire library of resources., connect with us, quick links.

• Explore Maths
• Explore Science
• Explore English

Or search by topic

Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

For younger learners

• Early Years Foundation Stage

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

Place Value and Powers

Dicey Operations   Age 11 to 14 Challenge Level

Always a Multiple?   Age 11 to 14 Challenge Level

Method in Multiplying Madness?   Age 7 to 14 Challenge Level

Power Countdown   Age 14 to 16 Challenge Level

Power Mad!   Age 11 to 14 Challenge Level

Short Problems   Age 11 to 14

• Place Value, Integers, Ordering & Rounding
• Number Operations & Calculation Methods
• Powers and Roots
• Indices and Surds

Counting in Powers of 10: Reasoning and Problem Solving

• Home Learning
• Free Resources
• New Resources
• Free resources
• New resources
• Filter resources
• Childrens mental health
• Easter resources

Internet Explorer is out of date!

For greater security and performance, please consider updating to one of the following free browsers

Counting in Powers of 10 Year 5 Place Value Resource Pack

Step 8: Counting in Powers of 10 Year 5 Resources

Counting in Powers of 10 Year 5 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Autumn Block 1.

Not a member? Sign up here.

What's included in the pack?

This pack includes:

• Counting in Powers of 10 Year 5 Teaching PowerPoint.
• Counting in Powers of 10 Year 5 Varied Fluency with answers.
• Counting in Powers of 10 Year 5 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 5: (5N1)  Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000

Mathematics Year 5: (5N5)  Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

Mathematics Year 5: (5N6)  Solve number problems and practical problems that involve 5N1 - 5N5

Differentiation:

Varied Fluency Developing  Questions to support completing sequences counting forwards and backwards in powers of 10 up to 1,000,000, when the rule has been given. No negative numbers. Expected  Questions to support completing sequences counting forwards and backwards in powers of 10 up to 1,000,000, when the rule is not always given. Including negative numbers up to -100. Greater Depth  Questions to support completing sequences counting forwards and backwards in powers of 10 up to 1,000,000, when the rule has not been given. Including negative numbers up to -1,000.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing  Use digit cards to create numbers following a sequence. Sequence rule counts forwards or backwards in powers of 10 up to 1,000,000. Rule given. Expected  Use digit cards to create numbers following a sequence. Sequence rule counts forwards or backwards in powers of 10 up to 1,000,000. Rule not given. Greater Depth  Use digit cards to create numbers following a sequence. Sequence rule counts forwards or backwards in powers of 10 up to 1,000,000. Rule not given and may include negative numbers up to -1,000.

Questions 2, 5 and 8 (Problem Solving) Developing  Calculate the amount required to get from one given amount to another when counting backwards or forwards in powers of 10 up to 1,000,000. Rule given. Expected  Calculate the amount required to get from one given amount to another when counting backwards or forwards in powers of 10 up to 1,000,000. Rule not given and may include negative numbers up to -100. Greater Depth  Calculate the amount required to get from one given amount to another when counting backwards or forwards in powers of 10 up to 1,000,000. Rule not given and may include negative numbers up to -1000.

Questions 3, 6 and 9 (Reasoning) Developing  Explain who is correct when given two statements relating to a sequence. Sequence rule adds or subtracts powers of 10 up to 1,000,000. Expected  Explain who is correct when given two statements relating to a sequence. Sequence rule adds or subtracts powers of 10 up to 1,000,000 and may include negative numbers up to -100. Greater Depth  Explain who is correct when given two statements relating to a sequence. Sequence rule adds or subtracts powers of 10 up to 1,000,000 and may include negative numbers up to -1,000.

This resource is available to download with a Premium subscription.

Our Mission

To help our customers achieve a life/work balance and understand their differing needs by providing resources of outstanding quality and choice alongside excellent customer support.​.

Yes, I want that!

Keep up to date by liking our Facebook page:

Membership login, stay in touch.

01422 419608

[email protected]

Interested in getting weekly updates from us? Then sign up to our newsletter here!

Information

• Cookie Policy
• Privacy Policy
• Terms and Conditions

Copyright: Classroom Secrets 2024

Company number: 8401067

VAT number: 248 8245 74

• Terms & Conditions

Designed by Classroom Secrets

Talk to our experts

1800-120-456-456

Power of 10

Introduction to Power of 10

The power of ten, in math, any of the integer (whole-valued) exponents of the number 10. A power of 10 is as many number 10s as designated by the exponent multiplied together. Therefore, shown in long-form, a power of ten is the number 1 subsequent to n zeros, in which ‘n’ is the exponent and is greater than 0; for example, 10 6 is mathematically written as 1,000,000. When n is less than 0, the power of 10 is the number 1 n placed followed by the decimal point; for example, 10 −3 is written 0.001.

Power of 10 to Zero

When n equals to 0, the power of 10 will be 1; i.e., 10 0 = 1. Refer to the below table for expressions in positives and negative powers of 10.

Powers of 10

Multiplying and Dividing Powers of 10

Maybe you're not sure that it's useful to be able to write numbers in powers of ten math or mega 10 powers. Well, powers of ten math are quite helpful when performing math calculations, as well. Let's say if we ask you ''what are 10 times 1,000?'' Hardly anything- it's just 10,000. But what if we ask ''what will be one trillion times one quadrillion?''

It concludes that the multiplication of really large numbers is easy with powers of ten. All you need to do is to add up the exponents, and you're sorted. Let's consider the example we just quoted above. What is one trillion times one quadrillion? First, one trillion is 10 12 , and one quadrillion is 10 15 . So the correct answer is 10 27 , which is a huge number. Now, you can see that almost immediately, without requiring a calculator, we did it shorthand.

Power of Ten Prefixes

When a numerical digit represents a quantity instead of a count, SI prefixes can be used - therefore "femtosecond", not "one quadrillionth of a second'' - although most frequently powers of 10 are used rather than some of the very low and very high prefixes. In certain cases, specialized units are taken help of, such as the light-year particle physicists barn or the astronomer's parsec.

Nonetheless, large numbers carry an intellectual intrigue and are of mathematical interest, and assigning them names is one of the ways in which most of us try to conceptualize and understand them.

Solved Examples

Solve the following expressions:

Log (10 6 ) = 6

Log (10 27 ) = 27

Log (10 365.2748 ) = 365.2748

Log (10 -5 ) = -5

Log (x) -5 → x = 10 5

Log (x) = 6.789 → x = 10 6.789

Log (x) = -2.23 → x = 10 -2.23

The power of 10 is easy to remember since we use base 10 of a number system.

For 10 n having ‘n’ a positive integer, just write "1" with n zeros after it. For negative powers 10 −n , write “0" followed by n−1 zeros, and then a 1. The powers of 10 are extensively used in scientific notation.

Let's take a number 10. We could take two 10s and multiply them together, which means 10 times 10, which you know is equal to 100. We could also take three 10s and multiply them together, 10 times 10 times 10 which is equal to one thousand. And we could do this with any number of 10s. But at some point, if we do this with enough 10s, it will get pretty hard for us to write. So let's give an example. Let's say I were to do this with ten 10s, so if I were to go 10 times 10 just like this :  10×10×10×10×10×10×10×10×10. This is going to be equal to even the number that is equal to, is going to be quite hard to write. It is  going to be one that is followed by ten zeros. This will be 10 billion. And it's already getting hard to write. And imagine if you have thirty 10s that we were multiplying together, it will be very much difficult to calculate or write down like this.

The mathematicians have come up with some notations and some ideas to be able to write things like this, a little bit more elegantly. So the way they do this is through something which is  known as exponents. And so 10 times 10, we can rewrite as being equal to, if I have two 10s and I'm multiplying them together, I could write this as 10 to the second power. That's how we can pronounce it as 10 to the power 2. It looks quite fancy but all that means is let's take two 10s and multiply them together and we are going to get one hundred. In this, the two would be called as exponents and the 10 would be the base. So eventually, 10 to the second power of 10 times 10 is equal to hundred. 

So how would you write 10 times 10 times 10 or 10000 ? How are you going to write that by using exponents ? We are taking three numbers of 10s and multiplying them together, this would be 10 to the third power. Here, ten is the base and three is the exponent. We would read this as 10 to the third power. If you will ever see 10 to the third power, that means we can multiply 10 times 10 times 10 which is the same thing as one thousand. So this is another way of writing 1000. 

FAQs on Power of 10

1. What is Meant by Logarithm?

Logarithm, the power or exponent to which a base should be raised to produce a given number. Written mathematically, x is the logarithm of n to the base b if b x = n, where case one writes x = log b n. For example, 2 4 = 16; thus, 4 is the logarithm of 16 to base 2, or 4 = log 2 16. Similarly, since 10 3 = 1000, then 3 = log 10 1000. Logarithms of the second-mentioned sort (that is, logarithms with base 10) are known as common, or Briggsian, logarithms and are simply written log n.

2. What is the importance of ‘logs’ in powers?

Are you assuming if there's an opposite to powers of 10? Something like how multiplication is the opposite of division or addition is the opposite of subtraction. It appears that there is such a thing called: ``logs'' or “logarithms”. Logs initially emerged to be important for multiplying and dividing and were used all the time in performing arithmetic operations with the help of slide rules. Now that calculators are commonplace, the use of logarithms for fundamental calculations is steadily disappearing, but it can still be worthwhile. And while employing logarithms for simple arithmetic calculations is not so common, there are other uses for logarithms in many areas of science.

You'll need JavaScript enabled to experience the full functionality of this site. Please enable JavaScript by following the instructions at enable-javascript.com .

Sorry, the browser you're currently using is not supported by this site. Please upgrade your browser by following the instructions at browser-update.org .

Powers of 10 — Problem Solving (Year 6)

Write a review

Choose your format:

Save to Your Lessons

Save to Homework

Share resource

Your download limit has been reached!

Check out our FAQs for more info. 

This resource is suitable for the White Rose Maths Scheme of Learning, covering Autumn Term Block 1 (Place value), Step 4 (Powers of 10).

Develop children’s understanding of powers of 10 with this worksheet. They must answer questions about a place value chart and find the missing numbers in the calculations.

Answers are provided.

This resource is also available in a handy Lesson Pack, containing a selection of brilliant worksheets for this small step.

View Lesson Pack    See all Year 6 White Rose

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: White Rose Maths | Autumn Term: Place Value | Small Step 4
• Topic Group: Number and Place Value
• Year(s): Year 6
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 24/10/2023
• Resource Code: M2WAT14021
• Curriculum Point(s): Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit. Solve number and practical problems that involve number and place value.

Related Topics:

Other Teachers Downloaded...

Powers of 10 — Function Machines (Year 6)

• White Rose Maths | Autumn Term: Place Value | Small Step 4
• Key Stage 2 Maths

Powers of 10 — Function Machines: Stretch (Year 6)

Powers of 10 — Function Machines: Foundation (Year 6)

Escape Room Rounding (Year 6)

• White Rose Maths | Autumn Term: Place Value | Small Step 7

Rounding Large Numbers (Year 6)

Rounding Large Numbers: Stretch (Year 6)

No reviews (yet!)

Related Resources

Place Value: Autumn Term — Small Step 4 (Year 6)

• Lesson Pack

• Solving Problems

• Multiplication & Division

Place Value: Autumn Term — Small Step 1 (Year 6)

• White Rose Maths | Autumn Term: Place Value | Small Step 1

Roll and Record — 7 Digit Numbers (Year 6)

• White Rose Maths | Autumn Term: Place Value | Small Step 2

Rounding to 10 and 100 (Year 4)

Let's Go Round Again — Rounding Large Numbers (Year 6)

Cookies are disabled on your browser. This means some features of the site won't be fully available to you.

CGP uses cookies to give you a smooth shopping experience and to help us understand how well our site is working. To agree to us using all cookies, click 'Accept', or to reject optional cookies click 'Customise'.

Accept cookies Customise cookies

• International
• Education Jobs
• Schools directory
• Resources Education Jobs Schools directory News Search

Mastery in maths - year 5 counting in powers of 10 fluency, reasoning and problem solving questions

Subject: Mathematics

Age range: 7-11

Resource type: Assessment and revision

Last updated

22 February 2018

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Tes paid licence How can I reuse this?

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

This resource hasn't been reviewed yet

To ensure quality for our reviews, only customers who have purchased this resource can review it

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: