Calculators guide
How to Convert a Decimal to a Fraction (Including Repeating Decimals)
Turn any decimal into a simplified fraction: the three-step method, mixed numbers, the algebra trick for repeating decimals, a chart of common values and inch fractions.
By M2Toolkit Editorial TeamPublished 5 min read
Quick answer
Write the decimal over 1, multiply the top and bottom by 10 for every digit after the decimal point, then simplify by dividing both by their greatest common divisor. For 0.75: 75/100, and since both divide by 25, 0.75 = 3/4.
Converting decimals to fractions comes up in homework, recipes, woodworking and any time a measurement is in inches. Terminating decimals like 0.625 take one step. Repeating decimals like 0.333… need a small algebra trick. Both are covered below, with a chart of the conversions you'll use most.
Terminating decimals: three steps
- 1Count the digits after the decimal point. 0.625 has three.
- 2Write the digits over 1 followed by that many zeros: 625/1000.
- 3Divide the top and bottom by their greatest common divisor (GCD). The GCD of 625 and 1000 is 125, so 0.625 = 5/8.
If you don't spot the GCD straight away, keep dividing by small common factors. 625/1000 → 125/200 (÷5) → 25/40 (÷5) → 5/8 (÷5).
Try the free Decimal to Fraction ConverterType any decimal, including repeating ones, and get the simplified fraction with the working.Decimals bigger than 1 and mixed numbers
Convert the part after the point, then put the whole number back in front:
To go from a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator: 2 × 8 + 3 = 19, so 19/8.
Repeating decimals: the algebra trick
Let x be the decimal, multiply so the repeating part lines up, then subtract to cancel it:
10x = 3.333…
10x − x = 3 → 9x = 3 → x = 3/9 = 1/3
When the repeat starts later, as in 0.1666…, multiply twice so the repeating parts match:
100x = 16.666… and 10x = 1.666…
100x − 10x = 15 → 90x = 15 → x = 15/90 = 1/6
Common decimals as fractions
| Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|
| 0.1 | 1/10 | 0.5 | 1/2 |
| 0.125 | 1/8 | 0.625 | 5/8 |
| 0.2 | 1/5 | 0.666… | 2/3 |
| 0.25 | 1/4 | 0.75 | 3/4 |
| 0.333… | 1/3 | 0.8 | 4/5 |
| 0.375 | 3/8 | 0.875 | 7/8 |
Inches and the nearest fraction
Tape measures use halves, quarters, eighths and sixteenths, so a decimal measurement often has to be rounded to the nearest one. Multiply the decimal by 16 and round: 0.3125 × 16 = 5, so 0.3125 in is exactly 5/16 in. For 0.43 in: 0.43 × 16 = 6.88, which rounds to 7, so about 7/16 in.
Some decimals have no exact fraction at all. π and √2 are irrational, so any fraction is an approximation. 22/7 is close to π, and 355/113 is correct to six decimal places.
Try the free Fraction CalculatorAdd, subtract, multiply or divide fractions and mixed numbers, simplified automatically.Frequently asked questions
What is 0.6 as a fraction?
6/10, which simplifies to 3/5.
What is 1.25 as a fraction?
1 1/4 as a mixed number, or 5/4 as an improper fraction.
How do I convert a percentage to a fraction?
Divide by 100 first: 45% = 0.45 = 45/100 = 9/20.
Why does 0.999… equal 1?
Using the trick: x = 0.999…, 10x = 9.999…, so 9x = 9 and x = 1. The two are the same number written differently.