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.