Percent to Fraction Calculator: simplest form, mixed number and decimal
Convert a percentage to a fraction in simplest form, a mixed number and a decimal, with the steps. Works with decimal percents like 35.5%, repeating percents like 33.3…% (1/3) and percents over 100%, or finds the nearest simple fraction.
How it works
Fraction = percent ÷ 100 → write over 100 × 10^k (k = decimal places) → divide top and bottom by their GCF · Repeating: p = (N − M) ÷ (10^k − 10^(k−r)) ÷ 100, where N is the digits through one repeating block and M is N with the r repeating digits removed · Mixed number = whole part + remainder/denominator
“Percent” means “per hundred”, so every percentage is already a fraction with 100 on the bottom. To convert, write the percentage over 100. If it has decimal places, multiply the top and bottom by 10 for each place so the top becomes a whole number (35.5/100 becomes 355/1000). Then divide both by their greatest common factor to reach the simplest form. A result above 1 (any percentage over 100%) is also shown as a mixed number, and the decimal is the percentage divided by 100. Repeating percentages such as 33.333…% or 16.666…% cannot be written exactly with a finite number of digits. Choose Repeating and say how many final digits repeat: the calculator uses the standard subtraction method to cancel the endless tail and returns the exact fraction (1/3, 1/6). If you only want a handy fraction close to a measured percentage, choose Approximate and set the largest denominator; the best fraction comes from the continued-fraction expansion, so no closer fraction exists with a smaller or equal denominator. The arithmetic uses exact whole numbers, so long decimals reduce without rounding error. Very long inputs are rounded to 10 decimal places first.
Worked example
Convert 62.5% (the default). Write it over 100: 62.5/100. It has one decimal place, so multiply top and bottom by 10: 625/1000. The greatest common factor of 625 and 1000 is 125, and 625 ÷ 125 = 5 and 1000 ÷ 125 = 8, so 62.5% = 5/8. As a decimal, 62.5 ÷ 100 = 0.625, and as a ratio 5 : 8. With Repeating chosen, 33.3 with one repeating digit means 33.333…%: 10 × p = 333.3…, 1 × p = 33.3…, so 9p = 300, p = 300/9 percent = 300/900 = 1/3.
Sources: CalculatorSoup: Percent to Fraction Calculator (method and examples) · Inch Calculator: Percent to Fraction Calculator (conversion chart) · Percentage (Wikipedia)
Frequently asked questions
How do I convert a percent to a fraction?
Write the percentage over 100 and simplify. For 45%, 45/100 has a greatest common factor of 5, so it reduces to 9/20. For 25%, 25/100 reduces by 25 to 1/4.
How do I convert a percentage with a decimal, like 35.5%?
Multiply the top and bottom by 10 for each decimal place first. 35.5% = 35.5/100 = 355/1000, and dividing by the common factor 5 gives 71/200. The calculator counts the decimal places for you.
What is 33.33% as a fraction?
Exactly as typed, 33.33% is 3,333/10,000. But 33.33% is usually a rounded one third: 33.333…% repeating is exactly 1/3. Choose Repeating with 1 repeating digit to get 1/3, or Approximate to find the nearest simple fraction.
How do I write a percentage over 100% as a fraction?
The same way: it becomes an improper fraction, which you can also write as a mixed number. 125% = 125/100 = 5/4 = 1 1/4, and 250% = 5/2 = 2 1/2. A whole hundred, like 200%, reduces to the whole number 2.
What does simplest form mean?
A fraction is in simplest (lowest) terms when the top and bottom have no common factor other than 1. Dividing both by their greatest common factor gets you there in one step: for 625/1000 that factor is 125, giving 5/8.
How do I turn a fraction back into a percent?
Divide the top by the bottom and multiply by 100. 5/8 = 0.625, and 0.625 × 100 = 62.5%.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.