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Convert percents to fractions

Percent notation represents a quantity per hundred, so a percent can be written as a fraction with denominator 100 and then expressed in an equivalent simplified form, such as 25%=25100=1425\%=\frac{25}{100}=\frac14. The understanding applies to whole-number and familiar finite decimal percents in ordinary part-to-whole contexts, emphasizing that the percent sign cannot simply be removed; generalized symbolic forms and more advanced percentage cases are outside this scope.

Detailed Explanation: Convert percents to fractions

A percent means “per hundred.” To convert a percent to a fraction:

  1. Write the percent number as the numerator.
  2. Write 100100 as the denominator.
  3. Simplify the fraction if possible.

Example: Convert 35%35\% to a fraction.

Write 35%35\% as a fraction over 100100:

35%=3510035\%=\frac{35}{100}

Now simplify 35100\frac{35}{100}. Both 3535 and 100100 are divisible by 55:

35÷5100÷5=720\frac{35\div 5}{100\div 5}=\frac{7}{20}

Therefore,

35%=720\boxed{35\%=\frac{7}{20}}

Remember: the percent sign cannot simply be removed. It tells you to use 100100 as the denominator first.

Learn by doing: Convert percents to fractions

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    Percents to Fractions - Powers of Ten

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