Float to Fraction Calculator

Example Data Table

Formula Used

For an exact terminating decimal, the decimal is written as digits over a power of ten. Then both values are reduced.

Fraction = integer made from digits / 10^{decimal places}

Simplified fraction = numerator ÷ GCD / denominator ÷ GCD

For a repeating decimal with whole part A, non-repeating digits B, repeating digits C, non-repeating length n, and repeating length r:

Fraction = [A × 10ⁿ(10^r - 1) + B(10^r - 1) + C] / [10ⁿ(10^r - 1)]

Approximation mode uses continued fractions. It searches for a close numerator and denominator within the selected limit.

How to Use This Calculator

1. Enter the float, decimal, or signed value.
2. Select exact, approximate, or repeating mode.
3. Add repeating digits only when the decimal repeats forever.
4. Set a maximum denominator for practical approximation.
5. Press the calculate button and review the result above the form.
6. Use the export buttons to save the current result.

Float to Fraction Guide

Floats are decimal numbers used in calculators, spreadsheets, code, and measurement tools. They are easy to type, but they can hide the exact ratio behind a value. A fraction can show that ratio clearly. This calculator converts a float into a simplified numerator and denominator. It also supports mixed numbers, repeating parts, and denominator limits.

Why Fraction Output Matters

Fractions are useful when a decimal comes from a real scale, a recipe, a drawing, or a finance model. A value such as 0.125 is clearer as 1/8. A value such as 2.75 is often better as 2 3/4. Engineers, teachers, woodworkers, cooks, and students use these forms because they are readable and exact.

Exact Decimal Conversion

For a normal terminating float, the method counts the digits after the decimal point. The decimal is then written over a power of ten. After that, the numerator and denominator are divided by their greatest common divisor. This step removes common factors and returns the simplest fraction.

Repeating Decimal Support

Some decimals continue forever. Examples include 0.333... and 1.1666.... The repeating option lets you enter the recurring block separately. The calculator builds a fraction using the non-repeating digits and the repeating digits. This avoids rough guesses and gives a dependable exact result.

Approximation Controls

Not every entered float should be treated as exact. Many values come from instruments or rounded reports. The maximum denominator setting helps create a practical fraction instead of a huge one. A smaller limit gives simpler output. A larger limit gives closer output. Tolerance controls how close the fraction must be to the original decimal.

Reading the Answer

The result panel shows the simplified fraction first. It also shows the improper fraction, mixed number, decimal check, and error. The decimal check converts the fraction back to a decimal. The error shows the difference between the entered float and the produced fraction. A zero error means the conversion is exact.

Best Use Cases

Use this tool for education, spreadsheet cleanup, unit conversion, machining notes, recipes, probability, and math homework. It is also helpful when decimal values must be shown in a more traditional format. When the source decimal is rounded, use approximation mode. When the source decimal is written exactly, use exact mode.

Precision Tips

Start with the exact option when the decimal was typed from a known value. Use approximation when the decimal came from a sensor, chart, or rounded average. For inch-style work, try denominators such as 16, 32, 64, or 128. For school math, a high limit is usually fine. Always compare the decimal check with the original float before copying the answer. This habit prevents hidden rounding mistakes. Keep negative signs with the whole value, not only the numerator. That makes the final fraction easier to read. Save exports when records need later review too.

FAQs