Decimal to Fraction Converter
Convert any decimal to a fraction in lowest terms or any fraction to a decimal.
Handles terminating and repeating decimals with step-by-step simplification.
Converting between decimals and fractions allows you to work with numbers in whichever form a calculation requires. Decimals are convenient for calculators; fractions preserve exactness for repeating values.
Decimal to Fraction — the method:
Step 1: Write the decimal as a fraction over 1. 0.625 = 0.625/1
Step 2: Multiply numerator and denominator by 10 for each decimal place. 0.625 has 3 decimal places → multiply by 1000: 625/1000
Step 3: Simplify by dividing by the Greatest Common Divisor (GCD). GCD(625, 1000) = 125 625/125 = 5, 1000/125 = 8 Answer: 5/8
Terminating decimals (like 0.625) always convert to exact fractions.
Repeating decimals (like 0.333…) require algebra: Let x = 0.333… 10x = 3.333… 10x − x = 3.333… − 0.333… 9x = 3 x = 3/9 = 1/3
Fraction to Decimal: Simply divide the numerator by the denominator. 7/16 = 7 ÷ 16 = 0.4375
Common conversions:
- 0.1 = 1/10
- 0.2 = 1/5
- 0.25 = 1/4
- 0.5 = 1/2
- 0.75 = 3/4
- 0.125 = 1/8
- 0.333… = 1/3
- 0.666… = 2/3
When to use fractions vs decimals: Use fractions when you need exact values (1/3 of a recipe), when simplifying algebraic expressions, or when the result will be used in further exact calculations. Use decimals for calculator work, measurements, and when a numerical answer is needed. Financial calculations typically use decimals rounded to 2 decimal places.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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