Fraction, decimal and percent converter
Type a fraction, a decimal or a percent, get the other two.
How do I convert a fraction to a percent?
Divide the top by the bottom and multiply by 100: 3/8 = 0.375 = 37.5%.
How do I convert a percent to a fraction?
Put the percent over 100 and simplify: 45% = 45/100 = 9/20.
How do I convert a percent to a decimal?
Divide by 100 — move the decimal point two places left: 7.5% = 0.075.
What is 1/3 as a percent?
33.33…% — the 3 repeats forever, written 33.(3)% here. 2/3 is 66.(6)%.
What about percents over 100?
They work the same way: 150% = 1.5 = 3/2, or 1 1/2.
Why does 5/7 give a repeating decimal but 3/8 does not?
A fraction in lowest terms terminates exactly when its denominator has no prime factors except 2 and 5 (Wolfram MathWorld, “Decimal Expansion”). 8 = 2³, so 3/8 ends at 0.375. 7 is prime, so 5/7 = 0.(714285) never ends; its six digits repeat, and as a percent it is 71.(428571)%, or about 71.43%. OpenStax rounds the same value to 71.4%.
How do I enter a mixed number, or a repeating decimal?
Type a mixed number with a space, as 1 3/8, and the calculator reads it as 11/8 = 1.375 = 137.5%. For a repeating decimal, put the repeating digits in brackets: 0.(142857) is 1/7, and 0.(3) is 1/3.
What is a percent below 1%?
0.5% = 0.5/100 = 1/200, which is 0.005 as a decimal. OpenStax’s exercises include 1.5%, which is 0.015 or 3/200.
The rules and what the calculator does
A percent is a ratio with a denominator of 100; “percent” means per hundred (OpenStax Prealgebra 2e, section 6.1). So a fraction becomes a percent by dividing the top by the bottom and multiplying by 100, a percent becomes a fraction by writing it over 100 and simplifying, and moving between a decimal and a percent shifts the point two places. The calculator has one box and reads what you type: a slash means a fraction, a percent sign means a percent, and anything else is a decimal. It then shows the fraction in lowest terms, the mixed number, the decimal and the percent. Digits that repeat are put in brackets, and a separate row gives the percent rounded to two decimal places.
Worked example: 5/7 and 24.5%
For 5/7, divide 5 by 7 to get 0.714285714285…, so the decimal is 0.(714285). Multiplying by 100 moves the point two places, giving 71.(428571)%, or 71.43% to two decimals. Going the other way, 24.5% is 24.5/100 = 245/1000, and dividing top and bottom by 5 gives 49/200; as a decimal it is 0.245. Both results agree with the OpenStax examples.
Common mistakes
Dropping the percent sign. Typing 37.5 is read as the decimal 37.5, which is 3750%, not 37.5%. Rounding too early: 1/3 is 33.(3)%, and using 33% instead makes 33% of 300 equal 99, not 100. Forgetting to multiply by 100, so that 3/8 = 0.375 is reported as 0.375%. And assuming a percent can’t exceed 100: 135% is simply 1.35, or 1 7/20.
Sources: OpenStax, Prealgebra 2e, section 6.1 “Understand Percent” (percent as a ratio to 100, conversions between fractions, decimals and percents); Wolfram MathWorld, “Decimal Expansion” (terminating and repeating decimals). Related tools: percentage calculator, decimal to fraction calculator, fraction calculator and long division calculator. How we check our calculators.