How to convert a decimal to a fraction
Here it is with your numbers:
- 0.625 has 3 decimal places, so write 625 over 1,000: 625/1000
- The greatest common factor (GCF) of 625 and 1000 is 125. Divide both by 125: 5/8
It means 0.625 and 5/8 are the same number.
Dividing the top and bottom by their greatest common factor gives the simplest form in one step. The GCF Calculator shows how to find it.
How to turn a repeating decimal into a fraction
A repeating decimal, like 0.333… or 0.1666…, goes on forever, but it is still a fraction. The trick is to subtract the repeating part away. Here is 0.1666…:
Here it is with your numbers:
- x = 0.166666…
- 10x = 1.66666…
- 100x = 16.6666…
- 100x − 10x = 16.6666… − 1.66666…
- 90x = 15
- x = 15/90
- The greatest common factor (GCF) of 15 and 90 is 15. Divide both by 15: 1/6
It means 0.166666… and 1/6 are the same number.
Type your own repeating decimal in the calculator to see these steps with your number.
Source OpenStax Algebra and Trigonometry 2e · 13.4 Series: a repeating decimal as a fraction (Example 8) ↗Common Core State Standards · Grade 8, repeating decimals are rational numbers (8.NS.A.1) ↗
Decimal to fraction chart
Common decimals as fractions in simplest form. Tap one to see the steps.
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.125 | 1/8 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.333… | 1/3 |
| 0.375 | 3/8 |
| 0.4 | 2/5 |
| 0.5 | 1/2 |
| 0.6 | 3/5 |
| 0.625 | 5/8 |
| 0.666… | 2/3 |
| 0.7 | 7/10 |
| 0.75 | 3/4 |
| 0.8 | 4/5 |
| 0.875 | 7/8 |
| 0.9 | 9/10 |
FAQs
How to convert decimal to fraction?
Count the decimal places, then write the digits without the point over 1 followed by that many zeros, and simplify. 0.625 has three decimal places, so it is 625/1000; both divide by 125, which gives 5/8.
How to change repeating decimals into fractions?
Call the number x and multiply it by 10 for each repeating digit, so the repeats line up. For 0.333…, 10x is 3.333…; subtracting x leaves 9x = 3, so x = 3/9, which is 1/3. With digits before the repeat, like 0.1666…, multiply twice (10x and 100x) and subtract those.
Source OpenStax Algebra and Trigonometry 2e · 13.4 Series: a repeating decimal as a fraction (Example 8) ↗
How to convert infinite decimals to fractions?
Only if they repeat. A decimal that goes on forever without repeating can’t be written as a fraction: it is not a rational number. Every fraction’s decimal either ends or repeats.
Sources
- OpenStax Contemporary Mathematics: 3.4 Rational Numbers: converting a terminating decimal to a fraction
- OpenStax Algebra and Trigonometry 2e: 13.4 Series: a repeating decimal as a fraction (Example 8)
- Common Core State Standards: Grade 8, repeating decimals are rational numbers (8.NS.A.1)