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Multiplying and dividing decimals by 10, 100 and 1000

Multiplying and dividing decimals by 10, 100 and 1000

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Explainer Video

Tutor: Labib

Summary

Multiplying and dividing decimals by 10, 100 and 1000

​​In a nutshell

Decimal numbers are numbers with digits which are not zero after a decimal point. To multiply or divide decimals by 10,100,1000,10,100,1000,10,100,1000, you must use place values to move the decimal place a certain number of places to the left or right.



Multiplying decimals by 10, 100, 1000

To multiply decimals by 10,100,100010,100,100010,100,1000​, follow this procedure:


PROCEDURE

​​​​×10\times10×10​​

Move the decimal point one place to the right.

​×100\times 100×100​​

​Move the decimal point two places to the right.

​×1000\times 1000×1000​​

​Move the decimal point three places to the right.


Example 1

Calculate 2.25×10002.25 \times 10002.25×1000​. 


Identify the multiplier.

2.25×1000‾2.25 \times \underline{1000}2.25×1000​​ 

Move the decimal point three places to the right.

​2.2 5 ↷ 2.\overset{\curvearrowright\,\,\,\,\,}{2\thinspace 5 \thinspace}2.25↷​​

​2.2 5 0↷ ↷ 2.\overset{\curvearrowright\,\curvearrowright\,\,\,\,}{2\thinspace 5 \thinspace 0}2.250↷↷​​

​2.2 5 0 0↷↷↷ 2.\overset{\curvearrowright\curvearrowright\curvearrowright\,\,\,}{2\thinspace 5 \thinspace 0\thinspace0}2.2500↷↷↷

Complete the multiplication.

​2.25×1000=2250.0=2250‾\underline{ 2.25 \times 1000 = 2250.0 = 2250}2.25×1000=2250.0=2250​​​


Note: 000 is a placeholder which is used if you reach the end of a decimal number. If a 000 is at the very end of a decimal it can be removed from the final answer.



Dividing decimals by 10, 100, 1000

​To divide decimals by 10,100,100010,100,100010,100,1000​​, follow this procedure:


PROCEDURE

​​​​÷10\div10÷10​​

Move the decimal point one place to the left.

​÷100\div100÷100​​

​Move the decimal point two places to the left.

​÷1000\div1000÷1000​​

​Move the decimal point three places to the left.


Example 2

Calculate 422.5÷100422.5 \div100422.5÷100. 


Identify the number you are dividing by.

422.5÷100‾422.5 \div \underline{100}422.5÷100​​ 

Move the decimal point two places to the left.

​422 ↶.542\overset{ \curvearrowleft}{2\thinspace }.5422↶.5​​

​42 2↶↶.54\overset{\curvearrowleft \curvearrowleft}{2\thinspace 2 }.5422↶↶.5​​

Complete the division.

​422.5÷100=4.225‾\underline{422.5 \div 100 = 4.225}422.5÷100=4.225​


Note: Only the decimal point moves position when dividing by 10,100,100010,100,100010,100,1000.​


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Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Numbers to 10,000,000

Unit 1

Numbers to 10,000,000

Counting in powers of 10

Unit 2

Counting in powers of 10

Jump Ahead

Score 80% to jump directly to the final unit.

Optional

Multiplying and dividing decimals by 10, 100 and 1000

Unit 3

Multiplying and dividing decimals by 10, 100 and 1000

Final Test

Test reviewing all units to claim a reward planet.

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you multiply or divide decimals by 10, 100 or 1000?

To multiply or divide decimals by 10,100,1000, you must use place values to move the decimal place a certain number of places to the left or right respectively.

Why are there zeros at the end of some decimals?

Zero is a placeholder which is used if you reach the end of a decimal number.

What is a decimal?

Decimal numbers are numbers with digits which are not zero after a decimal point.

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