The powers of Ten
Multiply with Powers of Ten
The number 10 holds special properties for multiplication in our number system. Multiplying by the number 10 or any power of 10 has the effect of moving the decimal point of the number it is multiplied to. Here’s how it works:
Practice 1: Multiplying a Power of Ten to a Whole Number.
Calculate the following product by hand or using a calculator.
a. 17 x 100 b. 250 x 10,000 c. 3 x 1,000,000 d. 1,489 x 1,000
Multiplying by large powers of ten (those greater than 1), moves the decimal point to the right. If the number to which you are multiplying a power of ten is a whole number, you will not see a decimal point, but you can write one in, then add the required number of zeroes to the end.
| Suppose we want the solution of | 45 x 1,000 |
| Put a decimal point behind the last digit of the whole number. | 45. |
| After the decimal point, write in the same number of zeroes as in the power of ten. | 45.000 |
| Move the decimal point to the end of the number. | 45,000. |
Practice 2: Multiplying a Power of Ten to a Whole Number.
Calculate the following product by hand or using a calculator.
a. 150 x 0.001 b. 12 x 0.00001 c. 79 x 0.1 d. 10,516 x 0.0001
When multiplying whole numbers by a power of ten, just imagine the decimal point behind the last digit and move the decimal according to the number of zeroes (for powers greater than 1) or the number of decimal places ( for powers less than 1).
Practice 3: Multiplying a Power of Ten to a Decimal.
Calculate the following product by hand or using a calculator.
a. 0.6 x 0.001 b. 27.45 x 0.00001 c. 0.081 x 10,000,000,000 d. 1.023 x 1,000
The pattern that emerges from the examples above gives us the following rules for multiplying with powers of ten.
When multiplying by a power of ten greater than one, move the decimal point one space to the right for every zero in the power. |
When multiplying by a power of ten less than 1, move the decimal point one space to the left for every decimal place in the power. |
Practice 4: Write each product using the rules for multiplying by powers of ten.
1. 3 x 100
4. 100 x 0.0001
7. 0.004 x 10,000,000
10. 12.03 x 102. 97 x 10,000
5. 0.2 x 1,000,000
8. 7.156 x 0.00001
11. 99.9 x 0.0013. 645 x 0.1
6. 34.8 x 1,000
9. 1.8 x 0.01
12. 300.1 x 0.1
