Decimals
Express a Decimal as a Fraction
To change a decimal to a fraction:
- Identify the place value of the last digit in the decimal.
- Drop the decimal point and write the number in the numerator of a fraction.
- In the denominator, write the positive power of ten that corresponds to the place value of the last digit. For instance, if the decimal’s last digit is in the thousandths place as in 0.258 put 1000 in the denominator. Examine the table below for more details.
| If the last digit is in . . . | The denominator is. . . |
| tenths | 10 |
| hundredths | 100 |
| thousandths | 1,000 |
| ten-thousandths | 10,000 |
| hundred-thousandths | 100,000 |
Example:
0.258 |
The eight is in the thousandths place, so we write: |
 |
2.36 |
The six is in the hundredth place , so we write: + |
 |
Notice in both examples the denominator is determined by how many numbers are AFTER the decimal point, not by how many numbers total.
Practice 1: Express the following decimals as fractions. Simplify your answer.
a. 0.448 b. 25.6 c. 3.0005 d. 0.08 e. 9.701
