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Percentage to Fraction

Convert any percentage to a fraction in its simplest form — including decimals like 12.5% and recurring ones like 33.3̄%.

%

Common percentages — click to convert

Step-by-step solution

Enter a percentage and press Convert to see the working

Per cent = per hundred

The word percent comes from Latin per centum — meaning out of 100. So every percentage is already a fraction over 100. The only job is to simplify it.

75% = 75/100 = 3/4 12.5% = 12.5/100 = 1/8 33.3̄% = 100/300 = 1/3

Examples

50% → 1/2 A common percentage, easily simplified by dividing 50/100 by their GCD of 50.
75% → 3/4 Another frequently encountered percentage. 75/100 simplifies to 3/4 by dividing by 25.
12.5% → 1/8 First, write as 12.5/100. To remove the decimal, multiply the top and bottom by 10 to get 125/1000, then simplify by dividing by 125.
0.5% → 1/200 Small decimal percentages follow the same rule: 0.5/100 becomes 5/1000, which simplifies to 1/200.
150% → 3/2 Percentages over 100% result in improper fractions (where the numerator is larger than the denominator). 150/100 simplifies to 3/2.
200% → 2/1 This means two whole amounts. 200/100 simplifies to 2/1, or simply 2.
33.3r% → 1/3 Recurring decimals require a special algebraic method to convert to a fraction before dividing by 100. 33.3r% is equivalent to 1/3.
66.6r% → 2/3 Another common recurring percentage. 66.6r% is equivalent to 2/3.

Percentage to Fraction Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

Where you already do this

You see "25% off" in a shop and instantly think "a quarter off" — that's converting a percentage to a fraction in your head. A nutrition label says "40% of your daily recommended iron" — that's 2/5. An opinion poll reports "33% support" — the exact fraction is ⅓. Converting percentages to fractions gives you the exact ratio behind the headline number.

Worked example

"Convert 40% to a fraction in its simplest form."

Step 1: Write over 100: 40/100

Step 2: Find GCD(40, 100) = 20

Step 3: 40 ÷ 20 = 2, 100 ÷ 20 = 5

Result: 2/5

Check: 2 ÷ 5 = 0.4 = 40% ✓

Common mistake to avoid

  • ✗ Not fully simplifying: 40/100 ÷ 2 = 20/50, which is technically correct but not in simplest form. Keep dividing until the GCD is 1. Using the GCD directly (20 here) does it in one step.
About

Percentage to Fraction Converter

Our Percentage to Fraction Converter helps you quickly change any percentage into its simplest fraction form. This tool is perfect for GCSE Maths students and anyone needing to understand the relationship between percentages and fractions.

The core idea is simple: 'percent' means 'per hundred'. So, 75% literally means 75 out of 100, which can be written as the fraction 75/100. The next step is always to simplify this fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). Our converter will show you the full working, including the Euclidean algorithm for finding the GCD.

It handles all types of percentages: simple whole numbers, decimals (like 12.5%), recurring decimals (like 33.3r%), and even percentages greater than 100% (like 150%).

Common mistakes to avoid

  • 75% = 75/100:While 75/100 is the correct initial step, the fraction is not in its simplest form. 75% = 75/100 = 3/4 (simplified by dividing numerator and denominator by 25).
  • 1% = 1:Forgetting that 'percent' means 'per hundred'. 1% is not a whole number. 1% = 1/100 (one out of a hundred).
  • 12.5% = 12.5/100:A fraction cannot have a decimal in its numerator or denominator. You need whole numbers. 12.5% = 125/1000 = 1/8 (multiply top and bottom by 10 to clear the decimal, then simplify).
  • 50% = 50/1:Confusing the 'per hundred' meaning with just putting the number over 1. This would mean 50 whole amounts. 50% = 50/100 = 1/2 (meaning 50 out of 100).
FAQ

Questions students ask

What does percent mean?
The word 'percent' comes from the Latin 'per centum', meaning 'per hundred' or 'out of every hundred'. So, a percentage is a way of expressing a number as a fraction of 100.
How do I convert a percentage to a fraction?
1. Write the percentage as a fraction with a denominator of 100 (e.g., 75% = 75/100). 2. If there's a decimal in the numerator (e.g., 12.5%), multiply both the numerator and denominator by 10 (or 100, 1000, etc.) until the numerator is a whole number (e.g., 12.5/100 becomes 125/1000). 3. Simplify the resulting fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For recurring decimals (like 33.3r%), you first convert the recurring decimal to a fraction using an algebraic method, then divide by 100.
What fraction is 33.3 recurring percent?
33.3 recurring percent (33.3r%) is equivalent to the fraction 1/3. This is a common recurring decimal that's useful to remember.
Can a percentage be greater than 100%?
Yes, absolutely! A percentage greater than 100% simply means you have more than a whole amount. For example, 150% means 1.5 times the original amount, or 3/2 as a fraction.
How do I convert a fraction back to a percentage?
To convert a fraction to a percentage, you simply multiply the fraction by 100. For example, to convert 3/4 to a percentage: (3/4) 100 = 75%. You can also convert the fraction to a decimal first (3 ÷ 4 = 0.75) and then multiply by 100 (0.75 100 = 75%).

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