How to convert decimal to fraction depends on what kind of decimal you have. Terminating decimals (like 0.75) become exact fractions by moving the decimal point; repeating decimals (like 0.333...) can also become exact fractions, but you need a repeating-decimal method instead. This guide focuses on both, with practical examples and a workflow for simplifying the final fraction.
Want a calculator-style converter? Use Decimal ↔ fraction to get simplified results instantly.
Key takeaways
- Terminating decimals → exact fractions with a power-of-10 denominator (then simplify).
- Repeating decimals → exact fractions, but use the repeating-decimal method (or algebra).
- Mixed numbers are just “whole part + fractional part” and can be represented as improper fractions when needed.
- Always simplify at the end (divide numerator and denominator by the greatest common divisor).
Step 1: identify the decimal type
Before converting, decide whether your decimal is:
- Terminating: ends after a finite number of digits (e.g. 0.125, 2.5).
- Repeating: one or more digits repeat forever (e.g. 0.333..., 0.142857142857...).
Terminating decimals: fastest exact method
For a terminating decimal, write it as a fraction with denominator equal to the power of 10 that matches the number of digits after the decimal point.
- Remove the decimal point to form the numerator.
- Use 10, 100, 1000, etc. as the denominator (depending on digits).
- Simplify the fraction.
Worked examples
Example 1: convert 0.75.
0.75 = 75/100 = 3/4.
Example 2: convert 2.125.
2.125 = 2125/1000 = 17/8 = 2 1/8 (mixed number form).
Repeating decimals: method for exact fractions
For repeating decimals, the numerator and denominator come from aligning one “repeat” of digits and subtracting, or from converting to an algebraic equation. A common reference method is:
- Let x equal the repeating decimal.
- Multiply x by the appropriate power of 10 so the repeating part lines up.
- Subtract to eliminate the repeating digits.
- Simplify the resulting fraction.
Quick reference example: 0.333... = 1/3.
Where rounding enters (and how to avoid it)
If your “decimal” came from measurement or from rounding a number upstream, it may be an approximation of a rational value. In that case, your fraction result can be a “best rational approximation” with a chosen maximum denominator. If you need the exact fraction, keep the original unrounded decimal information.
Next: convert the other way
If you also need the reverse conversion, see how to convert fractions to decimals.
Reference
For a worked walkthrough of converting terminating and repeating decimals, see Maths Is Fun: Convert Decimals to Fractions.
