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Fraction to Percent Calculator

Convert any fraction to a percent and a decimal, and see it in lowest terms.

What this tool does

Convert any fraction to a percent and a decimal, and see it in lowest terms. You fill in these fields: Numerator (top) and Denominator (bottom). It shows percent, decimal, and simplified fraction.

Inputs

  • Numerator (top): A whole number. The top number of the fraction. Whole numbers only.
  • Denominator (bottom): A whole number. The bottom number of the fraction. It cannot be 0.

How to use

  1. Enter the numerator (top).
  2. Enter the denominator (bottom).
  3. Read the result: percent, decimal, and simplified fraction. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Numerator (top): 3
  • Denominator (bottom): 4

Results:

  • Percent: 75.00%
  • Decimal: 0.75
  • Simplified fraction: 3/4

How this is worked out: greatest common divisor of 3 and 4 is 1, so the fraction is already in lowest terms: 3/4. Decimal = 3 / 4 = 0.75. Percent = 0.75 x 100 = 75.

Example 2. Inputs:

  • Numerator (top): 2
  • Denominator (bottom): 6

Results:

  • Percent: 33.33%
  • Decimal: 0.333333
  • Simplified fraction: 1/3

How this is worked out: greatest common divisor of 2 and 6 is 2, so 2/6 = 1/3. Decimal = 1 / 3 = 0.333... Percent = 0.333... x 100 = 33.333... The hero rounds this to 2 places, which gives 33.33.

Example 3. Inputs:

  • Numerator (top): -7
  • Denominator (bottom): 8

Results:

  • Percent: -87.50%
  • Decimal: -0.875
  • Simplified fraction: -7/8

How this is worked out: greatest common divisor of 7 and 8 is 1, so -7/8 stays as it is, with the sign on the top number. Decimal = -7 / 8 = -0.875. Percent = -0.875 x 100 = -87.5, which needs no rounding at 1 place.

Example 4. Inputs:

  • Numerator (top): 9
  • Denominator (bottom): 3

Results:

  • Percent: 300.00%
  • Decimal: 3
  • Simplified fraction: 3

How this is worked out: greatest common divisor of 9 and 3 is 3, so 9/3 = 3/1 = 3. Decimal = 3. Percent = 3 x 100 = 300. A whole result is shown as the text 3.

Where this comes from

A fraction as a percent. The fraction is written in lowest terms, and its numerator is taken as a percent of its denominator.

Write a fraction in lowest terms. The numerator and the denominator are both divided by their greatest common divisor. The sign is kept on the numerator. The denominator cannot be 0. Source: Arithmetic: a fraction is in lowest terms when its numerator and denominator have no common divisor above 1, reached by dividing both by their greatest common divisor.

What percent one number is of another. The part is multiplied by 100 and divided by the whole. The whole cannot be 0. Source: Arithmetic: a percent is a number of parts in one hundred, so part / whole x 100.

Limitations

  • Accepts whole numbers only for the top and the bottom. Decimals such as 0.5 are not accepted.
  • The bottom number cannot be 0.
  • Mixed numbers must be entered as improper fractions.
  • The percent is shown to two decimal places. The simplified fraction is always exact.

FAQs

Q: How is a fraction turned into a percent?
A: Divide the top number by the bottom number, then multiply by 100. Reducing the fraction first does not change the answer: 2/6 gives the same percent as 1/3.
Q: What does lowest terms mean?
A: It is the same fraction written with the smallest whole numbers. The top and bottom are divided by their greatest common divisor, so 6/8 becomes 3/4.
Q: Can I enter a mixed number such as 1 1/2?
A: No. Enter the improper fraction instead. For 1 1/2, enter 3 on top and 2 on the bottom.

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