Percents as Ratios

The word percent comes from the Latin per centum, which literally means 'by the hundred.' In mathematics, a percent is a ratio where the second number is always 100. We use the symbol $\%$ to show this. For example, if you see $7\%$, it is just a shortcut for the ratio $7:100$ or the fraction $\frac{7}{100}$. Because percents are based on 100, they make it very easy to compare different sizes. If one forest has $20\%$ oak trees and another has $30\%$, you know immediately which one has a higher concentration of oaks, even if the forests are different sizes!

Since percents, decimals, and fractions are just different ways to write the same value, we can switch between them. To turn a decimal into a percent, simply multiply by 100 (which is the same as moving the decimal point two places to the right) and add the $\%$ sign. To turn a fraction into a percent, the easiest way is to find an equivalent fraction with a denominator of 100. For example, $\frac{4}{5}$ can be multiplied by $\frac{20}{20}$ to get $\frac{80}{100}$, which is $80\%$. If the denominator doesn't easily go into 100, divide the top by the bottom to get a decimal first!

In the real world, we often need to find a percentage of a number that isn't 100. To find the percent of a quantity, follow this simple rule: Change the percent to a decimal and multiply it by the total amount. The word 'of' in math almost always means multiplication! For example, to find $20\%$ of $50$, you convert $20\%$ to $0.20$ and calculate $0.20 \times 50$. This allows you to calculate discounts, tax, or even how much battery life you have left on your phone.