Decimal to Fraction Converter — Simplification & Repeating Decimals

Converting a decimal back to a fraction takes a few more steps than going the other way, but it follows a reliable process. CalcHub's decimal to fraction converter does this instantly, including simplifying to lowest terms. If you want to understand the method, read on.

Method for Terminating Decimals

A terminating decimal has a finite number of digits (like 0.75 or 0.125). Steps:

1. Write the decimal as a fraction over 1: 0.75/1
2. Multiply numerator and denominator by 10 for each decimal place: 0.75 = 75/100
3. Simplify by finding the GCD (greatest common divisor): GCD(75,100) = 25
4. Divide both by GCD: 75/25 = 3, 100/25 = 4 → 3/4

Examples:

• 0.5 = 5/10 = 1/2
• 0.25 = 25/100 = 1/4
• 0.375 = 375/1000 = 3/8
• 0.625 = 625/1000 = 5/8
• 0.333 (approximate) ≈ 333/1000 (but 1/3 is exact — see repeating decimals below)

Common Decimals Reference Table

Decimal	Fraction	Simplified
0.1	1/10	1/10
0.125	125/1000	1/8
0.2	2/10	1/5
0.25	25/100	1/4
0.3	3/10	3/10
0.333…	—	1/3
0.375	375/1000	3/8
0.4	4/10	2/5
0.5	5/10	1/2
0.6	6/10	3/5
0.625	625/1000	5/8
0.666…	—	2/3
0.7	7/10	7/10
0.75	75/100	3/4
0.8	8/10	4/5
0.875	875/1000	7/8
0.9	9/10	9/10

Handling Repeating Decimals

For repeating decimals (like 0.333…), the terminating method doesn't work cleanly. Use algebra:

Example: convert 0.333… to a fraction

Let x = 0.333…
Then 10x = 3.333…
Subtract: 10x − x = 3.333… − 0.333…
9x = 3
x = 3/9 = 1/3

Example: convert 0.142857142857… to a fraction

This repeats a 6-digit block, so multiply by 10⁶:
Let x = 0.142857…
1,000,000x = 142857.142857…
999,999x = 142857
x = 142857/999999 = 1/7

Mixed Numbers

For decimals greater than 1, handle the integer and decimal parts separately.

• 2.75 → whole number = 2, decimal = 0.75 = 3/4 → result: 2 3/4
• 1.625 → whole = 1, decimal = 0.625 = 5/8 → result: 1 5/8
• 3.5 → whole = 3, decimal = 0.5 = 1/2 → result: 3 1/2

Simplifying Fractions

After converting, always simplify by dividing numerator and denominator by their GCD.

For 24/36:

• GCD(24, 36) = 12


• 24/12 = 2, 36/12 = 3 → simplified: 2/3

Quick GCD trick: use the Euclidean algorithm. GCD(24,36): 36 mod 24 = 12, 24 mod 12 = 0. GCD = 12.

How do I convert 0.666 (not repeating) to a fraction?

0.666 = 666/1000 = 333/500. Note: this is different from 0.666… (repeating), which is exactly 2/3. The truncated version 333/500 is a close approximation, not the exact fraction.

What fraction is 0.1875?

0.1875 = 1875/10000. GCD(1875, 10000) = 625. 1875/625 = 3, 10000/625 = 16. Answer: 3/16.

Can every decimal be written as a fraction?

Terminating and repeating decimals can always be written as exact fractions (rational numbers). Irrational numbers like π (3.14159…) or √2 (1.41421…) cannot — they don't repeat and never terminate.

Related Converters

• Fraction to Decimal Converter — forward direction
• Fraction Calculator
• GCD / LCM Calculator