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Multiplying and dividing by powers of 10

Multiplying and dividing by powers of 10

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Explainer Video

Tutor: Alice

Summary

Multiplying and dividing by powers of 10

​​In a nutshell

When multiplying or dividing by powers of 101010​, you will need to move the decimal point and potentially include some extra zeros. If you are multiplying, the decimal point moves towards the right as the number increases in value. If you are dividing, the decimal point moves towards the left as the number decreases in value.



Multiplying by powers of 10

​​Procedure

  1. Count the number of zeros the 10,100,100010, 100, 1000 10,100,1000 etc. has.
  2. Shift the decimal point of the number being multiplied by that many places to the right. If your decimal point reaches the end of the number, it helps to extend the number by writing in extra zeros at the end of the number, as required.
  3. The answer is the new number with the new location of the decimal point.


Example 1

What is 658.401×10000658.401 \times 10000658.401×10000?


100001000010000 has 444 zeros, hence move the decimal point 444 places to the right. As there are not 444 digits after the decimal point you can write 658.401658.401658.401 as 658.4010658.4010658.4010.


Shifting the decimal point 444​ places to the right gives 6584010‾\underline{6584010}6584010​.


​

Dividing by powers of 10

Procedure

  1. Count the number of zeros the 10,100,100010, 100, 100010,100,1000​ etc. has.
  2. Shift the decimal point of the number being multiplied by that many places to the left. If your decimal point reaches the end of the number, it helps to extend the number by writing in extra zeros at the beginning of the number, as required.
  3. The answer is the new number with the new location of the decimal point. If necessary, you may need to write a zero ahead of the decimal point.


Example 2

What is 7304.08÷1000007304.08\div 1000007304.08÷100000?


​100000100000100000 has 555 zeros, hence move the decimal point 555 places to the left. As there are not 555 digits ahead of the decimal point you can write 7304.087304.087304.08 as 07304.0807304.0807304.08


Shifting the decimal point 555​ places to the left gives 0.0730408‾\underline{0.0730408}0.0730408​.

​

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Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Multiplying and dividing decimals by 10, 100 and 1000

Unit 1

Multiplying and dividing decimals by 10, 100 and 1000

Multiplying and dividing by powers of 10

Unit 2

Multiplying and dividing by powers of 10

Jump Ahead

Score 80% to jump directly to the final unit.

Optional

Multiplying and dividing by powers of 10

Unit 3

Multiplying and dividing by powers of 10

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FAQs - Frequently Asked Questions

Does it matter if you do multiplication or division first?

Multiplication and division can be done together. In other words, it doesn't matter if you do division or multiplication first, but they must be done after brackets and indices and before addition and subtraction.

When you're multiplying does the order of the factors matter?

The commutative property says that the order of the numbers doesn't matter in multiplication.

What happens when you multiply by 10, 100 or 1000?

When you multiply whole numbers by 10, 100, 1000, you simply rewrite the numbers and put some extra zeros at the end. If you multiply a whole number by a 10, then you write one zero at the end.

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