The Decimal to Fraction Calculator converts any decimal number into its exact fractional or mixed number equivalent, and shows the complete step-by-step working — not just the answer. It handles three types of conversions that come up constantly in math:
0.75 → 3/4 or 16.66 → 16 33/500.333… → 1/3, where you specify how many trailing digits repeat1/8 or 1/16Working through fractions, algebra, or arithmetic who need to check their work or understand the method — not just get an answer.
A visual, step-by-step explainer to walk students through in class or assign for independent study.
Digital scales output decimals, but measuring cups use fractions like ¼ or ⅜ — this bridges the gap instantly.
Imperial measurements (inches, feet) are fraction-based. Decimal readouts from tools need quick, accurate translation.
Express a decimal proportion as a clean fraction for reports, presentations, or ratio analysis.
A professional explanation — as you would find in a math class
Every number can be expressed as a fraction. Begin by placing the decimal in the numerator and 1 in the denominator:
Count the digits after the decimal point. Multiply both numerator and denominator by 10 raised to that power. This shifts the decimal point right until it disappears. Multiplying top and bottom by the same number is equivalent to multiplying by 1 — the value stays identical.
16.66 has 2 decimal places → multiply by 10² = 100
Find the largest number that divides evenly into both numerator and denominator, then divide both by it. This reduces the fraction to its lowest terms.
GCF(1666, 100) = 2
When the numerator is larger than the denominator, the fraction is improper. Divide to extract the whole number part, and express the remainder as the new numerator.
833 ÷ 50 = 16 remainder 33
| Decimal places | Example | Multiply by |
|---|---|---|
| 1 | 0.5 | 10 |
| 2 | 0.25 | 100 |
| 3 | 0.125 | 1,000 |
| n | any | 10n |
Always simplify at the end. A fraction is not fully converted until it is expressed in its lowest terms — divide both parts by their Greatest Common Factor.