There are several different methods for converting decimals into fractions -- depending on whether or not the decimal number has digits to the left of the decimal point. I'll explain each scenario separately.
No Digits to the Left of the Decimal Point
If there are no digits to the left of the decimal point, you can simply restate the decimal number as a fraction. This is done by placing the number to the right of the decimal point as the numerator, and the denominator becomes a 1 followed by the number of zeros equal to the number of digits in the numerator, like this:
| .625 | = | 625 |
| 1000 |
Simply fraction if possible:
| 625 | = | 625 ÷ 125 | = | 5 |
| 1000 | 1000 ÷ 125 | 8 |
With or Without Digits to Left of Decimal Point
If there are one or more digits to the left of the decimal point (value greater than zero), the easiest way to convert the decimal to a fraction is to simply put the decimal number over the number one, and multiply the top and bottom of the fraction by a number that will cause the numerator to become an integer, like this:
| 3.625 |
| 1 |
Multiply top and bottom to get integer:
| 3.625 * 1000 | = | 3625 |
| 1 * 1000 | 1000 |
Simply fraction if possible:
| 3625 | = | 3625 ÷ 125 | = | 28 | = | 3 | 5 |
| 1000 | 1000 ÷ 125 | 8 | 8 |
Note that the number you multiply the top and bottom by is always a 1 with the same number of zeros added as the number of top digits. So if the top has 2 digits you would multiply the top and bottom by 100. If the top has 4 digits, you would multiply the top and bottom by 10000, and so on.
With Digits to Left of Decimal Point
If there are one or more digits to the left of the decimal point and their value is greater than zero, then the decimal can be restated as a mixed number, and in turn, that mixed number can be converted to a fraction, like this:
| 3.625 | = | 3 | 625 |
| 1000 |
Convert mixed number to fraction:
| 3 | 625 | = | 1000 * 3 + 625 | = | 3625 |
| 1000 | 1000 | 1000 |
Simply fraction if possible:
| 3625 | = | 3625 ÷ 125 | = | 28 | = | 3 | 5 |
| 1000 | 1000 ÷ 125 | 8 | 8 |
I hope I've explained the conversion process well enough for you to follow the steps. If not, please let me know in the feedback form located beneath the calculator.
