Decimal to Fraction

The decimal and fraction converter turns a decimal into a fraction and a fraction into a decimal. If the decimal never ends, the calculator finds its repeating part: ⁵/₆ = 0.8(3).

How to convert a decimal to a fraction

1. Write the number without the decimal point as the numerator.
2. Write 1 followed by as many zeros as there are digits after the point as the denominator.
3. Simplify the fraction.

Example. 0.375 = ³⁷⁵/₁₀₀₀ = ³/₈ (simplified by 125)
2.75 = ²⁷⁵/₁₀₀ = ¹¹/₄ = 2³/₄

How to convert a fraction to a decimal

Method 1. Divide the numerator by the denominator using long division.

Method 2. If the denominator has only 2s and 5s as prime factors, scale the fraction so that the denominator becomes 10, 100, 1000…

Example. ³/₈ = ^{3 · 125}/_{8 · 125} = ³⁷⁵/₁₀₀₀ = 0.375

When the decimal repeats forever

Simplify the fraction and factor the denominator into primes:

• only 2s and 5s — the decimal terminates: ⁷/₂₀ = 0.35;
• any other factors (3, 7, 11…) — the decimal repeats: ¹/₃ = 0.333… = 0.(3), ⁷/₁₂ = 0.58(3).

The repeating group of digits is called the period and is written in brackets. Converting a repeating decimal back to a fraction is done by a separate repeating decimal calculator.

Handy equivalents