Conversion entre fractions, décimales et pourcentages

Fractions, decimals, and percentages are three different ways of expressing the same value. Being able to convert fluently between them is a foundational math skill that appears in school, work, and everyday life. This guide provides clear conversion methods, worked examples, and a reference table for the most common values.

To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100. For example, 3/4 = 3 ÷ 4 = 0.75, and 0.75 × 100 = 75%. This two-step process works for any fraction: 2/5 = 0.40 = 40%, 7/8 = 0.875 = 87.5%, and 1/3 = 0.333... ≈ 33.33%. The 'X is what percent of Y' mode on our free percentage calculator does this automatically: enter the numerator as X and the denominator as Y.

To convert a percentage to a fraction, divide by 100 and simplify. 60% = 60/100 = 3/5. 12.5% = 12.5/100 = 125/1000 = 1/8. To simplify, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. According to the National Council of Teachers of Mathematics (NCTM), fraction simplification is a key skill that reinforces understanding of number relationships.

To convert a decimal to a percentage, multiply by 100 (or equivalently, move the decimal point two places to the right). 0.45 = 45%. 0.08 = 8%. 1.25 = 125%. To convert a percentage to a decimal, divide by 100 (move the decimal point two places to the left). 72% = 0.72. 5% = 0.05. 150% = 1.50.

To convert a fraction to a decimal, simply divide: 5/8 = 5 ÷ 8 = 0.625. To convert a decimal to a fraction, write the decimal as a fraction over a power of 10 and simplify: 0.625 = 625/1000 = 5/8. For repeating decimals, the conversion is more involved: 0.333... = 1/3, and 0.1666... = 1/6.

Here is a reference table of common conversions that are worth memorizing: - 1/2 = 0.50 = 50% - 1/3 ≈ 0.333 ≈ 33.33% - 2/3 ≈ 0.667 ≈ 66.67% - 1/4 = 0.25 = 25% - 3/4 = 0.75 = 75% - 1/5 = 0.20 = 20% - 2/5 = 0.40 = 40% - 3/5 = 0.60 = 60% - 4/5 = 0.80 = 80% - 1/8 = 0.125 = 12.5% - 3/8 = 0.375 = 37.5% - 5/8 = 0.625 = 62.5% - 7/8 = 0.875 = 87.5% - 1/10 = 0.10 = 10% - 1/100 = 0.01 = 1%

Mixed numbers convert by separating the whole number and fractional parts. For 2 3/4: the fractional part is 3/4 = 0.75, so 2 3/4 = 2.75 = 275%. Numbers above 100% simply represent values greater than 1 whole (or greater than the reference amount).

Percentages greater than 100% and less than 0% have specific meanings. 150% means 1.5 times the reference value — if your investment returned 150%, it grew to 2.5 times the original (the original plus 150% of it). Negative percentages represent decreases: −25% means a value dropped to 75% of the original, equivalent to the fraction 3/4. Understanding these edge cases is important for interpreting financial returns and percentage change calculations.

Repeating decimals and their percentage equivalents often trip up students. 1/6 = 0.16666... = 16.67% (rounded). 1/7 = 0.142857142857... ≈ 14.29%. 1/9 = 0.111... ≈ 11.11%. 1/11 = 0.0909... ≈ 9.09%. These are exact fractions with non-terminating decimals, so their percentage forms are approximations when expressed with finite decimal places. Khan Academy offers excellent lessons on recognizing which fractions produce terminating vs. repeating decimals — it depends on whether the denominator (in lowest terms) has only 2 and 5 as prime factors.

Practical applications of these conversions appear everywhere. In cooking, a recipe might call for 3/4 cup of flour. Knowing that 3/4 = 75% helps you scale the recipe: for 50% of the recipe, you need 75% × 0.50 = 37.5% of a cup, or 3/8 cup. In finance, an interest rate of 6.25% can be expressed as the fraction 1/16 (6.25/100 = 625/10000 = 1/16), which helps in mental estimation. In statistics, 'one in five' (1/5) is immediately recognized as 20%, making data more intuitive.

The relationship between fractions and percentages is also useful for estimation. Knowing that 1/3 ≈ 33% and 2/3 ≈ 67% lets you quickly gauge proportions. If 2 out of 3 dentists recommend a product, that is approximately 67% approval. If 3 out of 7 applicants are accepted, that is 3/7 ≈ 43% acceptance rate (since 3/7 is between 2/5 = 40% and 1/2 = 50%, closer to 3/7 ≈ 42.9%).

A useful trick for converting between fractions and percentages mentally: multiply the fraction by 100 using friendly decomposition. For 7/20: 7/20 × 100 = 7 × 5 = 35%. For 3/8: 3/8 × 100 = 300/8 = 37.5%. For 5/6: 5/6 × 100 ≈ 83.3%. This method avoids decimal division entirely. For more mental math shortcuts with percentages, see our everyday percentage tips guide.

When working with data, choosing the right representation matters. Fractions communicate exact values (1/3 is precise; 33.33% is an approximation). Decimals work well in calculations and spreadsheets. Percentages are best for communication and comparison because humans intuitively understand them. A survey result of '62%' is immediately clear; '31/50' requires additional processing.

Mastering conversions between fractions, decimals, and percentages gives you mathematical fluency that serves you in school, work, and daily life. Whether you are computing a tip (what is 18% of this bill?), baking (half of 3/4 cup?), or interpreting data (what fraction of users converted?), these three representations are interchangeable tools for the same underlying concept. Use our free percentage calculator to verify any conversion — or simply divide and multiply to practice the skill yourself.