Decimal to Fraction Converter

Enter any decimal — terminating, repeating, or a mixed integer/decimal — to get the equivalent fraction in its simplest form. The converter shows the numerator, denominator, mixed-number form and full working, so you can verify the result by hand.

Enter a decimal

Terminating decimals and integer values are supported. Up to 10 decimal places are converted exactly.

Enter a decimal value and press Convert.

How decimal-to-fraction conversion works

Every terminating decimal can be written exactly as a fraction using powers of ten. The method is:

  1. Count how many digits are after the decimal point — call it n.
  2. Write the decimal as a fraction with denominator 10ⁿ.
  3. Simplify the fraction by dividing numerator and denominator by their GCD.

0.75 → 75 / 100 → gcd(75, 100) = 25 → 3 / 4

3.125 → 3125 / 1000 → gcd = 125 → 25 / 8 = 3 ⅛

Repeating decimals

Repeating decimals such as 0.333… or 0.142857 142857… cannot be represented by a finite power of ten, but they can still be converted exactly using an algebraic technique. This converter handles terminating decimals exactly; for repeating decimals you can use the fraction calculator after converting them manually, or enter the fraction directly.

Common decimal-to-fraction conversions

DecimalFractionMixed number
0.11/10—
0.251/4—
0.333…1/3—
0.51/2—
0.666…2/3—
0.753/4—
0.84/5—
1.53/21 ½
2.259/42 ¼
3.12525/83 ⅛

Worked examples

Example 1 — Simple decimal

Convert 0.75 to a fraction.

Two digits after the decimal → denominator is 100: 75/100. Simplifying: gcd(75, 100) = 25 → 3/4.

0.75 = 3/4

Example 2 — Three decimal places

Convert 3.125 to a fraction.

Three digits after the decimal → 3125/1000. gcd(3125, 1000) = 125 → 25/8 = 3 ⅛.

3.125 = 25/8 = 3 ⅛

Example 3 — Integer with decimal part

Convert 0.0625 to a fraction.

Four digits after the decimal → 625/10000. gcd(625, 10000) = 625 → 1/16.

0.0625 = 1/16

Common mistakes

  • Using the wrong power of ten. The denominator must have as many zeros as there are digits after the decimal point. 0.125 has three digits after the point, so the denominator is 1000, not 100 or 10000.
  • Forgetting to simplify. 50/100 should be reduced to 1/2. The converter always simplifies, but if you are working by hand, do not skip this step.
  • Confusing terminating and repeating decimals. 0.25 is exactly 1/4, but 0.333… is only approximately 1/3 — it is exactly 1/3 only when written as a repeating decimal.
  • Misplacing the decimal point in mixed values. 3.125 converts to 3125/1000, not 31250/10000 or 3125/100.

Fraction to Decimal Converter

The reverse conversion — fraction → decimal.

Fraction Calculator

Add, subtract, multiply and divide fractions.

Mixed Number Calculator

Convert between mixed numbers and improper fractions.

Greatest Common Factor Calculator

Find the divisor used when simplifying fractions.

Frequently asked questions

Count the number of digits after the decimal point (n). Write the decimal part over 10ⁿ, then simplify. Example: 0.25 → 25/100 → 1/4.

This converter handles terminating decimals exactly. Repeating decimals such as 0.333… are only finite approximations unless you express the repeating part. Known repeating patterns like 0.333… (= 1/3) and 0.666… (= 2/3) are recognised, and the converter reports the closest simple fraction. For other repeating decimals you can enter the fraction directly using the fraction calculator.

Up to 10 decimal places are converted exactly. Beyond that, double-precision floating-point arithmetic may introduce rounding errors, so the converter caps the input length to guarantee accuracy.

The converter always reduces the fraction to lowest terms. If it is already reduced (for example, 0.3 → 3/10), the fraction shown is already in simplest form.