Write Fractions and Decimals as Percents

Learning Outcomes

  • Convert decimals and fractions to percents

To convert a decimal to a percent, remember that percent means per hundred and [latex]100 \%=1[/latex]. If we multiply the decimal by [latex]100 \%[/latex] we are really multiplying by [latex]1[/latex].  This gives us an easy method to change a decimal to a percent.

Convert a decimal to a percent

  1. Multiply the decimal by [latex]100 \%[/latex]

example

Convert each decimal to a percent:

  • [latex]2.7[/latex]
  • [latex]0.053[/latex]

Do you see a pattern? When we converted a decimal to a percent, we moved the decimal point two places to the right and then inserted a percent sign.  Sometimes we need to add zeros at the end of a decimal in order to move the decimal point two places to the right.

[latex]0.175=17.5 \%[/latex]

[latex]1.3=1.30=130 \%[/latex]

[latex]0.073=7.3 \%[/latex]

try it

Often in determining a percent, we have a ratio whose denominator is not 100. In order to convert such a ratio to a percent, we first convert the ratio to a decimal.

example

In a survey of 450 residents of a city, 126 said they were dissatisfied with their local internet provider. Find the percent of those surveyed who were not satisfied with their local internet provider.

 

Convert a fraction to a percent

  1. Convert the fraction to a decimal
  2. Convert the decimal to a percent

Sometimes when changing a fraction to a decimal, the result continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the nearest cent (hundredths place). In many cases we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.

example

Write as a percent.  Round to the nearest tenth of a percent if necessary.

  • [latex]\frac{9}{64}[/latex]
  • [latex]\frac{2}{3}[/latex]
  • [latex]2 \frac{3}{4}[/latex]

try it