Decimal to Fraction Converter

Decimal → simplified fraction

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About Decimal to Fraction Converter

A decimal-to-fraction converter that transforms decimals into simplified fractions. Handles terminating decimals (0.25 = 1/4), repeating decimals (0.333... = 1/3), and negative numbers. Shows GCD simplification steps and mixed number form. All calculations are client-side. Essential for math education, cooking conversions, and engineering measurements.

Decimal to Fraction Converter Features

  • Simplify
  • Mixed number
  • Repeating
  • GCD steps
  • Negative
To convert 0.375 to a fraction: count decimal places (3), write 375/1000, simplify by GCD(375,1000)=125 → 3/8. For repeating: 0.333... → x=0.333..., 10x=3.333..., 9x=3, x=1/3. Mixed numbers: 2.75 = 2 + 3/4 = 11/4.

How to Use

Enter a decimal:

  • Input: Any decimal number
  • Output: Simplified fraction
  • Extra: Mixed number form

Conversion Method

  1. Count decimal places (d)
  2. Write as integer/10^d
  3. Find GCD of numerator and denominator
  4. Divide both by GCD

Repeating Decimals

0.̄6 = 6/9 = 2/3. 0.̄12 = 12/99 = 4/33. 0.1̄6 = (16−1)/90 = 15/90 = 1/6.

Step-by-Step Instructions

  1. 1Enter a decimal number.
  2. 2View the fraction result.
  3. 3Check simplification.
  4. 4See mixed number form.
  5. 5Review GCD steps.

Decimal to Fraction Converter — Frequently Asked Questions

How do I convert 0.125 to a fraction?+

0.125 = 125/1000. GCD(125,1000) = 125. So 125÷125 / 1000÷125 = 1/8.

Can all decimals be expressed as fractions?+

All terminating and repeating decimals are rational (can be fractions). Non-repeating, non-terminating decimals like π and √2 are irrational — they cannot be exactly expressed as fractions.

What is a mixed number?+

A whole number plus a proper fraction: 7/4 = 1¾. The whole part is the quotient, the fraction part is the remainder over the divisor.

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