Decimal to Fraction Calculator
Enter a decimal number to convert it to a fraction.
How to Convert a Decimal to a Fraction
Method
- Count the decimal places (n). Write the decimal over 10n.
- Simplify the fraction by dividing numerator and denominator by their GCD.
Examples
| Decimal | Fraction | Simplified |
|---|---|---|
| 0.5 | 5/10 | 1/2 |
| 0.75 | 75/100 | 3/4 |
| 0.333… | 1/3 | |
| 1.25 | 125/100 | 5/4 = 1 1/4 |
Related Calculators
How to Convert a Decimal to a Fraction
For terminating decimals, count the decimal places to determine the denominator. 0.75 has 2 decimal places → denominator is 100 → 75/100. Then simplify by dividing numerator and denominator by their GCF: GCF(75,100) = 25, so 75/100 = 3/4. For repeating decimals (like 0.333…), set x = 0.333…, multiply by 10 to get 10x = 3.333…, subtract: 9x = 3, so x = 1/3. This algebraic trick works for any repeating decimal.
Common Decimal to Fraction Conversions
| Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|
| 0.5 | 1/2 | 0.125 | 1/8 |
| 0.25 | 1/4 | 0.333… | 1/3 |
| 0.75 | 3/4 | 0.666… | 2/3 |
| 0.2 | 1/5 | 0.625 | 5/8 |
How to Convert Any Decimal to a Fraction
Converting a decimal number to a fraction requires identifying the place value of the last significant digit. For a terminating decimal, count the digits after the decimal point. Write the decimal digits as the numerator and use 1 followed by as many zeros as there are decimal places as the denominator. For example, 0.75 has two decimal places, so it becomes 75 over 100. Then simplify by dividing both numerator and denominator by their greatest common factor. The GCF of 75 and 100 is 25, giving the simplified fraction 3 over 4. For mixed decimals like 2.6, keep the whole number part and convert only the decimal portion: 2 and 6 tenths equals 2 and 3 fifths. Repeating decimals require a different technique: set the decimal equal to a variable, multiply by a power of 10 to shift the repeating block, subtract the original equation, and solve. For example, 0.333... repeated equals 1 over 3 exactly. Converting decimals to fractions is essential in cooking recipes, carpentry measurements, and any field where exact rational proportions matter more than decimal approximations that introduce rounding errors into cumulative calculations.
Common Decimal to Fraction Reference Table
| Decimal | Fraction | Simplified |
|---|---|---|
| 0.1 | 1/10 | 1/10 |
| 0.25 | 25/100 | 1/4 |
| 0.333... | — | 1/3 |
| 0.5 | 5/10 | 1/2 |
| 0.6 | 6/10 | 3/5 |
| 0.666... | — | 2/3 |
| 0.75 | 75/100 | 3/4 |
| 0.8 | 8/10 | 4/5 |
| 0.125 | 125/1000 | 1/8 |
| 0.375 | 375/1000 | 3/8 |
Simplifying Fractions After Conversion
After converting a decimal to a fraction, always simplify the result to its lowest terms. Find the greatest common factor of the numerator and denominator, then divide both by it. If the GCF is 1, the fraction is already in simplest form. For large numerators and denominators, use the Euclidean algorithm: repeatedly replace the larger number with the remainder when dividing it by the smaller number until the remainder is zero. The last non-zero remainder is the GCF. For instance, to simplify 48 over 72, divide 72 by 48 to get remainder 24; divide 48 by 24 to get remainder 0. The GCF is 24, so 48 over 72 simplifies to 2 over 3. Keeping fractions in simplified form makes further arithmetic easier and results more readable.
