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Pre-Algebra

Converting Fractions, Decimals, and Percents

Lesson

Fractions, decimals, and percents are three ways to write the same number. Learn to slide between them fluently and a lot of problems get easier.

12=0.5=50%\frac{1}{2} = 0.5 = 50\%

Fraction → Decimal

Divide the numerator by the denominator. 34=3÷4=0.75\frac{3}{4} = 3 \div 4 = 0.75.

Decimal → Percent

Multiply by 100 (move the decimal two places right). 0.6=60%0.6 = 60\%.

Percent → Decimal

Divide by 100 (move the decimal two places left). 35%=0.3535\% = 0.35.

Decimal → Fraction

Read the place value, then reduce. 0.4=410=250.4 = \frac{4}{10} = \frac{2}{5}.

Worked example — full chain

Convert 25\frac{2}{5} to a percent.

25=2÷5=0.4=40%\frac{2}{5} = 2 \div 5 = 0.4 = 40\%

Common conversions to memorize

  • 12=0.5=50%\frac{1}{2} = 0.5 = 50\%
  • 14=0.25=25%\frac{1}{4} = 0.25 = 25\%
  • 34=0.75=75%\frac{3}{4} = 0.75 = 75\%
  • 15=0.2=20%\frac{1}{5} = 0.2 = 20\%
  • 110=0.1=10%\frac{1}{10} = 0.1 = 10\%

How to type your answer

Type fractions as 3/4, decimals as 0.75, and percents as 75 (just the number — leave off the % sign).

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Convert 12 to a decimal.\text{Convert } \frac{1}{2} \text{ to a decimal.}

Problem 2

Convert 0.25 to a percent (no % sign).\text{Convert } 0.25 \text{ to a percent (no \% sign).}

Problem 3

Convert 50% to a decimal.\text{Convert } 50\% \text{ to a decimal.}

Problem 4

Convert 14 to a percent (no % sign).\text{Convert } \frac{1}{4} \text{ to a percent (no \% sign).}

Practice

Standard problems matching the lesson.

Problem 5

Convert 34 to a decimal.\text{Convert } \frac{3}{4} \text{ to a decimal.}

Problem 6

Convert 25 to a decimal.\text{Convert } \frac{2}{5} \text{ to a decimal.}

Problem 7

Convert 710 to a decimal.\text{Convert } \frac{7}{10} \text{ to a decimal.}

Problem 8

Convert 0.6 to a percent (no % sign).\text{Convert } 0.6 \text{ to a percent (no \% sign).}

Problem 9

Convert 0.08 to a percent (no % sign).\text{Convert } 0.08 \text{ to a percent (no \% sign).}

Problem 10

Convert 1.25 to a percent (no % sign).\text{Convert } 1.25 \text{ to a percent (no \% sign).}

Problem 11

Convert 75% to a decimal.\text{Convert } 75\% \text{ to a decimal.}

Problem 12

Convert 4% to a decimal.\text{Convert } 4\% \text{ to a decimal.}

Problem 13

Convert 150% to a decimal.\text{Convert } 150\% \text{ to a decimal.}

Problem 14

Convert 0.5 to a fraction (reduced).\text{Convert } 0.5 \text{ to a fraction (reduced).}

Problem 15

Convert 0.4 to a fraction (reduced).\text{Convert } 0.4 \text{ to a fraction (reduced).}

Problem 16

Convert 0.25 to a fraction (reduced).\text{Convert } 0.25 \text{ to a fraction (reduced).}

Problem 17

Convert 35 to a percent (no % sign).\text{Convert } \frac{3}{5} \text{ to a percent (no \% sign).}

Problem 18

Convert 910 to a percent (no % sign).\text{Convert } \frac{9}{10} \text{ to a percent (no \% sign).}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Convert 58 to a decimal.\text{Convert } \frac{5}{8} \text{ to a decimal.}

Problem 20

Convert 0.125 to a fraction (reduced).\text{Convert } 0.125 \text{ to a fraction (reduced).}

Problem 21

Convert 12.5% to a fraction (reduced).\text{Convert } 12.5\% \text{ to a fraction (reduced).}

Problem 22

Convert 720 to a percent (no % sign).\text{Convert } \frac{7}{20} \text{ to a percent (no \% sign).}

Problem 23

Convert 0.875 to a percent (no % sign).\text{Convert } 0.875 \text{ to a percent (no \% sign).}

Problem 24

Convert 1520 to a percent (no % sign).\text{Convert } \frac{15}{20} \text{ to a percent (no \% sign).}

Problem 25

Convert 0.85 to a percent (no % sign).\text{Convert } 0.85 \text{ to a percent (no \% sign).}

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