Multiplying by powers of ten
Follow the following shortcut when multiplying by powers of ten
Whole numbers multiplied by powers of 10
When multiplying a whole number by a power of ten, just count how many zero you have and attached that to the whole number
Examples:
1) 56 × 10
There is only one zero, so 56 × 10 = 560
2) 45 × 10,000
There are 4 zeros, so 45 × 10000 = 450000
3) 18 × 10,000,000
There are 7 zeros, so 18 × 10,000,000 = 180,000,000
Decimals multiplied by powers of 10
When multiplying a decimal by a positive power of ten (positive exponent), move the decimal point one place to the right for each zero you see after the 1
Examples:
1) 0.56 × 10
There is only one zero, so move the decimal point one place to the right.
0.56 × 10 = 5.6
2) 0.56 × 100
There are 2 zeros, so move the decimal point two places to the right
0.56 × 100 = 56
3) 0.056 × 1000
There are three zeros, so move the decimal point 3 places to the right.
0.056 × 1000 = 56
4) 0.056 × 100,000
0.056 × 100,000 = 0.056 × 1000 × 100 = 56 × 100 = 5600
When multiplying a decimal by a negative power of ten (negative exponent), move the decimal point one place to the left for each zero you see before the 1
Note that 0.1 = 10
^{1}, 0.01 = 10
^{2}, 0.001 = 10
^{3}, and so forth....
We call 10
^{1}, 10
^{2}, and 10
^{3} negative powers of 10 because the exponents are negative
Examples:
1) 56 × 0.1
There is only one zero, so move the decimal point one place to the left.
56 × 0.1 = 5.6
2) 560 × 0.01
There are 2 zeros, so move the decimal point two places to the left
560 × 0.01 = 5.6
2) 560 × 0.001
There are 3 zeros, so move the decimal point two places to the left
560 × 0.001 = 0.560
3) 0.56 × 0.1
There is only one zero, so move the decimal point one place to the left.
0.56 × 0.1 = 0.056
4) 0.56 × 0.01
There are 2 zeros, so move the decimal point two places to the left
0.56 × 0.01 = 0.0056
Any questions about multiplying by powers of ten? Let me know...

Dec 11, 17 08:45 AM
Learn how to estimate fractions with this easy to follow lesson.
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.