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Mathematics 2026-05-03 3 min read By Konvertibly Team

Decimal to Fraction Converter: Terminating, Recurring, and Mixed Numbers

Convert terminating and recurring decimals to fractions — step-by-step methods, simplification, and how to handle mixed numbers like 2.75.

Decimal to Fraction Converter: Terminating, Recurring, and Mixed Numbers

Converting Decimals to Fractions

Every terminating decimal and every recurring decimal can be expressed as an exact fraction. The method differs slightly depending on whether the decimal terminates or repeats.

Terminating Decimals

0.75 = 75/100 = 3/4  (divide by GCD=25)
0.125 = 125/1000 = 1/8
2.6 = 26/10 = 13/5  (or mixed: 2 3/5)

Recurring Decimals

0.333… = x
10x = 3.333…
10x − x = 3 → 9x = 3 → x = 3/9 = 1/3

0.142857142857… = 142857/999999 = 1/7

Mixed Recurring (partial repeat)

0.416666… (0.41̄6̄)
Let x = 0.416666…
100x = 41.6666… | 10x = 4.1666…
90x = 37.5 → x = 375/900 = 5/12

Mixed Numbers

3.25 → whole = 3, decimal = 0.25 = 1/4
Mixed: 3 1/4 | Improper: 13/4

Convert decimals to fractions: Free Decimal to Fraction Converter

Step-by-Step Conversion Method

To convert a terminating decimal to a fraction: (1) Write the decimal over its place value. 0.75 = 75/100. (2) Simplify by dividing by GCD: GCD(75,100) = 25, so 75/100 = 3/4. For a two-decimal number 0.ab, the denominator is 100. For three decimals 0.abc, it is 1000. For 0.625: 625/1000 ÷ 125 = 5/8. Verify: 5 ÷ 8 = 0.625 ✓

Converting Repeating Decimals

  • 0.333... = 1/3 (multiply both sides of x = 0.333... by 10, subtract x to get 9x = 3)
  • 0.666... = 2/3
  • 0.1666... = 1/6
  • 0.142857... = 1/7 (6-digit repeating cycle)
  • 0.0909... = 1/11 (99 in denominator for 2-digit repeat)
  • 0.272727... = 3/11

Frequently Asked Questions

Why simplify fractions?

Simplified fractions (in lowest terms) are easier to compare, add, subtract, and use in further calculations. 75/100 is equivalent to 3/4 but 3/4 is immediately recognisable as "three quarters" while 75/100 requires mental processing. In algebra and engineering, working in lowest terms reduces the risk of arithmetic errors from large numerators and denominators.

How do I convert a mixed number like 2.375 to a fraction?

Separate the whole number (2) from the decimal (0.375). Convert 0.375: 375/1000, divide by GCD 125 = 3/8. The mixed number is 2 and 3/8, or as an improper fraction: (2 × 8 + 3)/8 = 19/8. Verify: 19 ÷ 8 = 2.375 ✓

Are all fractions convertible to terminating or repeating decimals?

Yes. Every rational number (fraction of two integers) produces either a terminating or repeating decimal. Irrational numbers like π, √2, and e produce non-terminating, non-repeating decimals and cannot be expressed as fractions of integers.