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All courses Math Foundations · MF.RN.5 11 of 60
Convert among fractions, decimals, and percents and choose the most useful form for a task.

Convert a fraction to decimal and percent

Problem
Convert 3/5 to a decimal and a percent. Write your answers as an equivalence statement, including the percent sign.
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Hint

Start by rewriting 3/5 as 3 ÷ 5 so you can find its decimal form.

A fraction means division, and a percent is the same value written out of 100.

Solution walkthrough

01

Rewrite the fraction as division

\[\frac{3}{5}=3\div~5\]

A fraction means numerator divided by denominator. So to find the decimal form of \(\frac{3}{5}\), divide 3 by 5.

02

Find the decimal value

\[3\div~5=0.6\]

Dividing 3 by 5 gives \(0.6\). That means the decimal name for \(\frac{3}{5}\) is \(0.6\).

03

Change the decimal to a percent

\[0.6\times~100=60\]

Percent means out of 100. To write a decimal as a percent, multiply by 100 and use the percent sign. So \(0.6\) becomes \(60\%\).

04

Write the equivalence statement

\[\frac{3}{5}=0.6=60\%\]

This matches the question because it shows the fraction, its decimal form, and its percent form as equal names for the same value.

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Another way

  1. You can convert fifths to hundredths: \(\frac{3}{5}=\frac{3\times 20}{5\times 20}=\frac{60}{100}\). Then \(\frac{60}{100}=0.60=60\%\).

!

Common mistake

A common mistake is to write \(\frac{3}{5}=0.3\) by copying the numerator into the decimal. That is wrong because the decimal comes from dividing 3 by 5, and \(3\div 5=0.6\), not \(0.3\).