Decimal to Fraction Converter
Convert any terminating decimal into an equivalent fraction in its simplest form. Ideal for students, cooks, and engineers who need exact fractional representations.
About this calculator
Every terminating decimal can be written as a fraction by using a power of 10 as the denominator. If a decimal has n digits after the decimal point, multiply both the decimal value and 1 by 10ⁿ to get an integer numerator over 10ⁿ. Then reduce the resulting fraction by dividing both parts by their GCD. The formula is: fraction = (decimal × 10ⁿ) / 10ⁿ, then simplified by GCD. For example, 0.75 has 2 decimal places, so it becomes 75/100, and since GCD(75, 100) = 25, the simplified result is 3/4. Repeating decimals require a different algebraic approach and are not handled by this calculator.
How to use
Say you want to convert 0.625 to a fraction. The decimal has 3 digits after the point, so the denominator is 10³ = 1000. The numerator is 625, giving 625/1000. Next, find GCD(625, 1000) = 125. Divide both: 625 ÷ 125 = 5 and 1000 ÷ 125 = 8. The result is 5/8. Enter 0.625 in the decimal field and the calculator performs all these steps automatically.
Frequently asked questions
How do you convert a decimal to a fraction step by step?
Count the number of decimal places in your decimal — this tells you the power of 10 to use as the denominator. Write the digits (without the decimal point) as the numerator over that power of 10. Then simplify the fraction by dividing both the numerator and denominator by their GCD. For example, 0.4 becomes 4/10, which simplifies to 2/5.
Can you convert a repeating decimal to a fraction with this calculator?
This calculator is designed for terminating decimals — those that end after a finite number of digits, like 0.5 or 0.125. Repeating decimals such as 0.333... require an algebraic method: set x = 0.333..., multiply by 10 to get 10x = 3.333..., subtract to get 9x = 3, so x = 1/3. That process is outside the scope of this tool, which handles straightforward decimal-to-fraction conversion.
Why might someone need to convert a decimal to a fraction?
Fractions are often more precise and meaningful than decimals in practical contexts. In cooking, a recipe might call for 3/4 cup rather than 0.75 cups. In carpentry and manufacturing, fractional measurements (like 5/8 inch) are standard on imperial rulers and tools. In math class, fractions are required for exact answers in algebra and number theory. Converting decimals to fractions ensures you can work seamlessly across these contexts.