Probability and Counting Principles: Background You’ll Need 1

  • Change numbers between fractions, decimals, and percentages

Decimals to Percents

Converting a decimal into a percent is a straightforward process once you understand that ‘percent’ means ‘out of [latex]100[/latex]‘. This conversion is based on shifting the value of a decimal two places to the right to find its equivalent percent.

How To: Convert a Decimal to a Percent

  1. Express the Decimal as a Fraction: Start by writing the decimal as a fraction with 1 as the denominator.
  2. Adjust to a Denominator of [latex]100[/latex]: Since a percent is a fraction out of [latex]100[/latex], scale the fraction so that the denominator is [latex]100[/latex]. This may involve multiplying both the numerator and the denominator by an appropriate factor.
  3. Convert to Percent: Once the denominator is [latex]100[/latex], the numerator is the percent value. Write this number followed by the percent sign (%).
Convert each decimal to a percent:

  1. [latex]0.05[/latex]
  2. [latex]0.83[/latex]

To convert a mixed number to a percent, we first write it as an improper fraction.
Convert each decimal to a percent:

  1. [latex]1.05[/latex]
  2. [latex]0.075[/latex]

Fraction to Percents

The process of converting fractions to percents involves two main steps: changing the fraction into a decimal, and then transforming that decimal into a percent. Understanding that ‘percent’ means ‘per hundred’ simplifies the conversion, as you’re essentially finding out how many parts out of [latex]100[/latex] the fraction represents.

How To: Convert a Fraction to a Percent

  1. Convert the Fraction to a Decimal: Divide the numerator (the top number of the fraction) by the denominator (the bottom number of the fraction) to get a decimal.
  2. Multiply by [latex]100[/latex] to Find the Percent: Take the decimal result and multiply it by [latex]100[/latex]. Then, add the percent sign ([latex]\%[/latex]) to the product to express the answer as a percentage.
Convert each fraction or mixed number to a percent:

  1. [latex]{\Large\frac{3}{4}}[/latex]
  2. [latex]{\Large\frac{11}{8}}[/latex]
  3. [latex]2{\Large\frac{1}{5}}[/latex]

Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right.

Sometimes when changing a fraction to a decimal, the division 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 hundredths place. For most other cases in this book we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.