Fractions, decimals and percentages: the same number three ways, and how to convert

Three-quarters, 0.75 and 75% are the same quantity written for different purposes, and moving between them is a skill that comes up in recipes, discounts, grades, and every measurement in an imperial kitchen. This guide covers the conversions and the reasoning; the fraction calculator does the arithmetic and shows its working.

One number, three notations

A fraction is a division waiting to happen: 3/4 means 3 ÷ 4. A decimal is the result of doing it: 0.75. A percentage is that decimal scaled by 100 so it reads as "parts per hundred": 75%. Nothing changes but the notation. Fractions keep exactness (1/3 is exact; 0.333… is not), decimals make comparison and calculation easy, percentages make comparison intuitive for people.

Converting in every direction

• Fraction → decimal: divide the top by the bottom. 5/8 = 0.625.
• Decimal → percentage: multiply by 100 (move the point two places right). 0.625 → 62.5%.
• Percentage → decimal: divide by 100. 12.5% → 0.125.
• Decimal → fraction: write the digits over a power of ten and simplify. 0.125 = 125/1000 = 1/8.
• Percentage → fraction: over 100, then simplify. 40% = 40/100 = 2/5.
• Fraction → percentage: divide, then multiply by 100; or scale the fraction to a denominator of 100 when it divides evenly (3/20 = 15/100 = 15%).

Worth memorising: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125, 1/3 ≈ 0.333, 2/3 ≈ 0.667, 1/10 = 0.1.

Recurring decimals

A fraction whose simplified denominator has any prime factor other than 2 or 5 produces a decimal that repeats forever: 1/3 = 0.333…, 1/7 = 0.142857142857…, 2/9 = 0.222…. Going back is a trick: for 0.727272…, call it x, note that 100x = 72.7272…, subtract to get 99x = 72, so x = 72/99 = 8/11. For a decimal that terminates after being rounded (0.33 from a calculator), you can only guess the fraction; the calculator shows the exact form when the input is a fraction and flags rounding when it isn't.

Simplifying and comparing fractions

Divide top and bottom by their greatest common divisor: 18/24 → ÷6 → 3/4 (the GCD calculator finds it). To compare 5/8 and 2/3, either convert to decimals (0.625 vs 0.667) or cross-multiply (5 × 3 = 15 versus 2 × 8 = 16; the side with the larger product is larger: 2/3). Adding needs a common denominator — How to add fractions (and why the rule works) walks through it — and mixed numbers (1 ¾) convert to improper fractions (7/4) for any arithmetic. Ratios are fractions read sideways (Ratios explained: how to simplify, scale, and divide an amount in a given ratio).

Which form when

• Recipes and measurements: fractions (¾ cup, ⅝ inch) — the recipe scaler keeps them.
• Money and calculations: decimals.
• Change, discounts, rates, shares of a whole: percentages — and How to calculate percentages covers the traps, like a 50% rise followed by a 50% fall not returning to the start.
• Probability: fractions for exact odds (1/6), percentages for communicating them (16.7%).
• Exact maths: fractions, always — a decimal of 1/3 is already rounded.