8.1.5 Converting

Activity symbolActivity: Fractions, Decimals, and Percentages

[ Want to get more comfortable with converting among fractions, decimals, and percentages? Play this game! ] (a) In your math notebook, turn each of the given percentages into a decimal as well as into a fraction in lowest terms.

  • (i) 10%
  • (ii) 25%
  • (iii) 50%
  • (iv) 125%
  • (v) 0.5%
Hint symbol


To turn a percentage into a decimal, how far and in which direction should you move the decimal? To turn the percentage into a fraction, which number do you divide by? Don’t forget to reduce the fraction if possible.

Solution symbol



  • (i) Decimal: 10 percent equals 0.1 Fraction: 10 percent equation sequence equals 10 divided by 100 equals one divided by 10
  • (ii) Decimal: 25 percent equals 0.25 Fraction: 25 percent equation sequence equals 25 divided by 100 equals one divided by four
  • (iii) Decimal: 50 percent equals 0.5 Fraction: 50 percent equation sequence equals 50 divided by 100 equals one divided by two
  • (iv) Decimal: 125 percent equals 1.25 Fraction: 125 percent equation sequence equals 125 divided by 100 equals five divided by four
  • (v) Decimal: 0.5 percent equals 0.005 Fraction: 0.5 percent equation sequence equals 0.5 divided by 100 equals 0.5 multiplication two divided by 100 multiplication two equals one divided by 200

(b) Write each of the following given numbers as percentages.

  • (i) three divided by four
  • (ii) five divided by eight
  • (iii) one divided by three
  • (iv) 0.4
  • (v) 0.0075
  • (vi) 1.2
Hint symbol


There are several different ways of doing this. Do you like to go through a decimal? Do you prefer to multiply by 100%? (This last approach will be shown in the solutions.)

Solution symbol


(b) Multiplying each fraction or decimal by 100% gives the following answers:

  • (i) equation left hand side three divided by four equals right hand side three divided by four multiplication 100 percent equals 75 percent
  • (ii) equation left hand side five divided by eight equals right hand side five divided by eight multiplication 100 percent equals 62.5 percent
  • (iii) equation left hand side one divided by three equals right hand side one divided by three multiplication 100 percent equals percent
  • (iv) 0.4 equals 0.4 multiplication 100 percent equals 40 percent
  • (v) 0.0075 equals 0.0075 multiplication 100 percent equals 0.75 percent
  • (vi) 1.2 equals 1.2 multiplication 100 percent equals 120 percent

By no means did you have to do it this way, but don’t forget that your answer must include a percent symbol.

8.1.4 The Importance of the Percent Sign

8.1.6 Calculator Exploration: Percentage Conversions