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.
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...