Powers of 10 refer to 10,100,1000 and so on. To multiply and divide by powers of 10, you have to use place values to move the decimal place a certain number of steps to the left or right.
Multiplying by powers of 10
To multiply by powers of 10, follow this procedure:
procedure
Count how many zeros there are in the power of 10.
Move the decimal point to the right by the same amount.
Note: If the number is a whole number, then add ".000...", adding as many zeros as required.
Example 1
What is 3.2×1000?
First, count how many zeros are in 1000. Then, write 3.2 as 3.2000.. and move the decimal point 3 places to the right. Finally, get rid of the extra zeros past the decimal point.
Dividing by powers of 10
To divide by powers of 10, it is exactly the same as multiplying, except the decimal point moves the other way.
procedure
Count how many zeros there are in the power of 10.
Move the decimal point to the left by the same amount, adding zeroes to the left if necessary.
Example 2
What is 25÷100000?
First, count how many zeros there are in 100000. Then, write 25 as ...000025.0, and move the decimal point 5 places to the left. Get rid of the unnecessary zeros.
Multiplying and dividing by multiples of powers of 10
Multiples of powers of 10 refers to numbers such as: 30000,20,800 and so on. To multiply and divide by these numbers, first you have to multiply or divide by the multiple (the number "attached" to the power of 10).
Example 3
What is 400÷50000?
First, write 50000 as 5×10000.
To compute 400÷50000, first do 400÷5 and then divide the answer by 10000, using the method above:
400÷5=80
80÷10000=0.0080↶↶↶↶
80÷10000=0.008
400÷50000=0.008
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Length:
Unit 1
Counting in powers of 10
Unit 2
Multiplying and dividing decimals by 10, 100 and 1000
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Unit 3
Multiplying and dividing by powers of 10
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FAQs - Frequently Asked Questions
What is a power of 10?
A power of 10 refers to numbers such as: 10, 100, 1000 etc.
How do you divide by a power of 10?
Count how many zeros are in the power of 10, and move the decimal point to the left by the same amount.
How do you multiply by a power of 10?
Count how many zeros are in the power of 10, and move the decimal point to the right by the same amount.
