Decimals & percentages

A percent means “per 100,” so $25\%$ equals $\frac{25}{100}$ or $0.25$. You may switch among percent, decimal, and fraction forms to simplify a calculation. For example, $8\%$ of $50$ is $0.08\times 50$, but it is also $50\%$ of $8$, which is clearly $4$. To write a terminating decimal as a fraction, place it over a power of 10 and reduce: $0.125=\frac{125}{1000}=\frac{1}{8}$. For a repeating decimal such as $0.\overline{3}$, set it equal to $x$, multiply by a power of 10 to line up the repeating part, subtract, and solve for $x$. If a value increases and then decreases by percents, multiply the multipliers ($1.20\times 0.80=0.96$) instead of adding the percentages.