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Mom's Basement University

Converting Between Percent, Decimal, and Fraction

What You’ll Learn

Section titled “What You’ll Learn”

In this lesson you’ll learn simple rules to convert percentages to decimals and fractions, and back again.

The Concept

Section titled “The Concept”

Conversions are straightforward:

  • Percent to decimal: Move decimal point 2 places left (divide by 100). 45%→0.4545\% → 0.45

  • Percent to fraction: Put number over 100, simplify. 45%→45100=92045\% → \frac{45}{100} = \frac{9}{20}

  • Decimal to percent: Move decimal 2 places right (multiply by 100). 0.75→75%0.75 → 75\%

  • Fraction to percent: Divide numerator by denominator, then convert decimal to percent. 34=0.75=75%\frac{3}{4} = 0.75 = 75\%

  • Fraction to decimal: Divide numerator by denominator.

Worked Examples

Section titled “Worked Examples”

Convert each:

  1. 20%→20\% → decimal 0.20→0.20 → fraction 20100=15\frac{20}{100} = \frac{1}{5}
  2. 0.625→0.625 → percent 62.5%→62.5\% → fraction 6251000=58\frac{625}{1000} = \frac{5}{8}
  3. 25→\frac{2}{5} → decimal 0.4→0.4 → percent 40%40\%

Real-World Applications

Section titled “Real-World Applications”

Conversions help compare offers: 1/4 off = 0.25 = 25% discount. Or tax: 8% = 0.08, so 0.08×2000.08 \times 200 dollars = 16 dollars tax. Or interest: 6.5% = 0.065. Knowing how to switch makes shopping, budgeting, and finance clearer.

Quiz

Section titled “Quiz”
Convert 65% to a decimal.
What is 0.4 as a percent?
Convert 3/5 to a percent.
Convert 25% to a simplified fraction.
What is 15% of 200?