5.2 Converting Between Percents, Decimals, and Fractions (310)
Objectives: (310)
Change a percent to a fraction
Change a fraction to a percent
Change a percent, a decimal, or a fraction to equivalent forms
5,2,1 Changing a Percent to a Fraction (310)
Easy, just put the percentage over 100 (and simplify)
PP1. Write as a fraction in simplest form. (310) a.
71% = 71 / 100 b.
75% = 75 / 100 = 3 / 4 c.
8% = 8 / 100 = 2 / 25
Hint: Don’t forget to REDUCE after converting
If there are decimals in the percent, it is sometimes easier to write as a decimal first.
PP2. Write as fraction in simplest form (310) a.
8.4% = 0.084 = 84 / 1000 = 21 / 250 b.
28.5% = 0.285 = 285 / 1000 = 57 / 200
If it is above 100%, it will be written as a mixed number (or an improper fraction).
PP3. Write as a mixed number (or improper fraction) (310) a.
170% = 170 / 100 = 17 / 10 or 1 7/10 b.
288% = 288 / 100 = 72 / 25 or 2 22/25
If the percent has a fraction in it, convert to fractions
PP4. Convert 7 5/8% to a fraction in simplest form (311)
( 7 5/8 ) / 100 = (61 / 8) ÷ 100 = (61 / 8)(1 / 100) = 61 / 800
PP5. In the fiscal 2007 budget of the United States , approximately 20 7/8% was designed for
Social Security. Write the percent as a fraction. (311)
( 20 7/8 / 100) = (167 / 8) ÷ 100 = (167 / 8)(1 / 100) = 167 / 800
5.2.2 Changing a Fraction to a Percent (312)
Normally we will convert a fraction to decimal, then convert the decimal to percent
PP6. Write 5 / 8 as a percent; 5 ÷ 8 = 0.625 = 62.5%
PP7. Write as a percent a.
21 / 25 21 ÷ 25 = 0.86 = 86% b.
7 / 16 7 ÷ 16 = 0.4375 = 43.75%
Sometimes we get a repeating decimal. Hopefully they ask for the value rounded
PP8. Write as a percent. Round to the nearest 100 th . a.
7 / 9
7 ÷ 9 = 0.77777 = 77.777% = 77.78% b.
19 / 30 19 ÷ 30 = 0.63333 = 63.333% = 63.33%

On very rare occasions, they want the percent with a fraction [PS. I won’t test you on this]
PP9. Express 7 / 12 as a percent with a fraction. (314)
7 / 12 7 / 12 = .58 R 4 = 58 4 /12 % = 58 1/3%
5.2.3 Changing a Percent, a Decimal, or a Fraction in Equivalent Forms (314)
We saw this before. We change a fraction to a decimal to a percent.
PP10. Complete the table below. Round decimals to the nearest ten-thousandth. (315)
Fraction Decimal Percent
23 / 99 0.23232 23.23%
129/250 0.516 51.6%
97/250 0.172 17 1/5%
Alternate Method. We could use proportions instead. (315)
7 / 8 = x / 100; 8x = 700; x = 0.875 = 87.5%