Decimals and Percents.

A decimal, a fraction, and a percent are three ways of writing the same number.

$\frac{1}{2} \;=\; 0.5 \;=\; 50\%$

Fraction → decimal

Just divide the top by the bottom. $\frac{3}{4} \;=\; 3 \div 4 \;=\; 0.75$

Decimal → percent

Multiply by $100$ (or move the decimal two places right) and add the $\%$ sign. $0.75 \;\to\; 75\%$ $0.08 \;\to\; 8\%$ $1.2 \;\to\; 120\%$

Percent → decimal

Divide by $100$ (move decimal two places left) and drop the $\%$. $25\% \;\to\; 0.25$ $3\% \;\to\; 0.03$ $150\% \;\to\; 1.5$

Percent of a number

"$30\%$ of $50$" means $0.30 \times 50 = 15$.

The word "of" in percent problems means multiply. Convert the percent to a decimal first: $15\% \text{ of } 80 \;=\; 0.15 \times 80 \;=\; 12$

Common conversions worth memorizing

$\frac{1}{2} = 0.5 = 50\%$ $\frac{1}{4} = 0.25 = 25\%$ $\frac{3}{4} = 0.75 = 75\%$ $\frac{1}{5} = 0.2 = 20\%$ $\frac{1}{10} = 0.1 = 10\%$