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Decimal to Fraction Calculator

Convert any decimal to a simplified fraction or mixed number. Also shows percentage and nearest common fractions.

What is Decimal to Fraction Calculator?

A decimal to fraction calculator converts any decimal number — including repeating decimals — into a simplified fraction or mixed number. It finds the exact fraction by multiplying by a power of 10 to eliminate the decimal part, then reduces using the Greatest Common Divisor (GCD). It also shows the equivalent percentage and the nearest standard fractions (halves, quarters, eighths, sixteenths).

How to use

  1. 1 Enter any decimal number, such as 0.75, 1.333, or 3.14159.
  2. 2 The simplified fraction appears instantly — for example, 0.75 → 3/4.
  3. 3 If the value is greater than 1, the mixed number form is also shown (e.g., 1.25 → 1 1/4).
  4. 4 Scroll down to see the equivalent percentage and nearest common fractions.

Formula

For a terminating decimal with d decimal places: multiply by 10^d to get an integer numerator, use 10^d as denominator, then divide both by GCD. For repeating decimals (period p): numerator = (full number × 10^(non-repeating + repeating digits) − full number × 10^non-repeating digits) / (10^p − 1), then simplify.

Example calculation

0.75 → 75/100 → GCD(75,100)=25 → 3/4. 1.333… → repeating digit 3, period 1 → (13−1)/9 = 12/9 → GCD(12,9)=3 → 4/3 = 1 1/3. 0.625 → 625/1000 → GCD=125 → 5/8.

Frequently asked questions

How do you convert a decimal to a fraction?

Write the decimal digits as the numerator (ignoring the decimal point) and use 10^(number of decimal places) as the denominator. Then simplify by dividing both by the GCD.

How do you convert a repeating decimal to a fraction?

Let x = the repeating decimal. Multiply by 10^p (where p is the repeat length) to shift one full cycle, then subtract the original equation to eliminate the repeating part. Solve for x and simplify.

What is a mixed number?

A mixed number combines a whole number and a proper fraction — for example, 1 3/4. It represents the same value as the improper fraction 7/4.

How accurate is the fraction conversion?

For terminating decimals the result is exact. For long non-repeating decimals (like π), the calculator finds the best rational approximation for the digits you enter.

What are the nearest common fractions?

These are the closest fractions from the set 1/2, 1/4, 3/4, 1/8, 3/8, 5/8, 7/8, 1/16, … to your decimal. They are useful in cooking, woodworking, and other practical applications.