A percent is a type of ratio where something is compared to a hundred. Probabilities, scores, and success rates are commonly written in percents.
Conversion to Fractions and Decimals
By definition, means , which means hundredths. In other words, converting percents to decimals means moving two decimal places to the left, and converting decimals to percents means moving two decimal places to the right. For instance, , , and .
Percent of a Number
Let be the percentage, be the number we want to take the percentage of, and be the wanted quantity. By definition, , so . In other words, to find the percent of the number, we convert the percent to the fraction (or decimal) and then multiply it with the number we want to take the percentage of. For example, of equals .
The percent change equals the ratio of the positive difference between the original quantity and the new quantity to the original quantity when written as a percent. For example, the percent change from 10 to 15 equals .
Percent Increase and Decrease
If the new quantity is greater than the original quantity, then the percent change is called a percent increase. If the new quantity is smaller than the original quantity, then the percent change is called a percent decrease.
Let be the percentage, be the new quantity, and be the old quantity. From the definition of percent change, a percent increase is written in the form , and solving for results in . Additionally, a percent decrease is written in the form , and solving for results in .
For a written example, a increase from is , and a decrease from is .