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Convert percents to fractions

Percent is understood as a rate per hundred: p%p\% denotes the rational number p100\frac{p}{100}, so conversion preserves the quantity represented rather than merely removing the percent symbol. Whole-number and simple terminating-decimal percents, including values greater than 100%100\%, can be expressed as equivalent simplified proper or improper fractions, supporting comparison and proportional reasoning; repeating-decimal and more advanced symbolic cases are outside this scope.

Detailed Explanation: Convert percents to fractions

A percent means “per 100.” Therefore, to change a percent to a fraction, write the number before the percent sign over 100100, then simplify.

Example: Convert 125%125\% to a fraction.

  1. Write 125125 over 100100:
125%=125100 125\%=\frac{125}{100}
  1. Simplify the fraction. Both 125125 and 100100 are divisible by 2525:
125÷25100÷25=54 \frac{125\div25}{100\div25}=\frac{5}{4}

Therefore,

125%=54\boxed{125\%=\frac{5}{4}}

This fraction is improper because 125%125\% is greater than 100%100\%. It can also be written as the mixed number 1141\frac14.

Learn by doing: Convert percents to fractions

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    Percents to Fractions - Powers of Ten

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