Percentages

Percent means "per hundred" (out of 100).

$25\% = \frac{25}{100} = 0.25$

Converting Between Forms

Percent to Decimal

Divide by 100 (move decimal 2 places left): $45\% = 0.45$ $8\% = 0.08$ $125\% = 1.25$

Decimal to Percent

Multiply by 100 (move decimal 2 places right): $0.73 = 73\%$ $0.04 = 4\%$ $1.5 = 150\%$

Percent to Fraction

Put over 100 and simplify: $75\% = \frac{75}{100} = \frac{3}{4}$

Fraction to Percent

Convert to decimal, then to percent: $\frac{3}{5} = 0.6 = 60\%$

Finding Percentages

"What is 15% of 80?"

Convert percent to decimal, then multiply: $15\% \times 80 = 0.15 \times 80 = 12$

Finding the Percent

"What percent of 40 is 8?"

$\frac{8}{40} = 0.2 = 20\%$

Percent Increase/Decrease

Percent Change = $\frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%$

Example: Price goes from $50 to $65 $\frac{65 - 50}{50} \times 100\% = \frac{15}{50} \times 100\% = 30\% \text{ increase}$

Common Percentages