Formula
0.d₁d₂…dₖ = (d₁d₂…dₖ) ÷ 10ᵏ0.a(b) = ((ab − a) ÷ (10ᵏ·(10ᵐ − 1))) in general form
- k — number of digits after the decimal point
- m — number of repeating digits
Write the digits over 1 followed by as many zeros as there are decimal places, then divide top and bottom by their greatest common divisor.
Worked examples
0.75
- Decimal
- 0.75
Fraction
3/4
Mixed number: 3/4
Percentage: 75%
0.1666… (6 repeating)
- Decimal
- 0.1
- Repeating digits
- 6
Fraction
1/6
Mixed number: 1/6
Percentage: 16.66666667%
How it works
0.75 has two decimal places, so it is 75/100. The greatest common divisor of 75 and 100 is 25, which gives 3/4. Everything is done with exact integers, so there is no floating-point guesswork.
Repeating decimals use a different identity: 0.(3) means 0.333… and equals 3/9 = 1/3; 0.1(6) is 0.1 followed by repeating 6 and equals 1/6. Enter 0.1 as the decimal and 6 as the repeating digits.
If you type a rounded value like 0.3333, the exact fraction is 3333/10000. The tool also shows the closest simple fraction with a denominator up to 1,000 (1/3), which is usually what you meant. To convert in the other direction see Fraction to Decimal Calculator.
Assumptions and limits
- Up to 30 digits are accepted.
- Without repeating digits, the decimal is treated as exact, not rounded.