2-2 Percents Greater Than 100% and Less Than 1%

Property

$100\% = 1$ (the complete whole)
This means that 100% represents the entire quantity or the complete amount of something.

Examples

Property

A percent greater than 100% represents a value greater than 1. When the part is greater than the whole, the ratio $\frac{\text{part}}{\text{whole}}$ will be greater than 1, resulting in a percent greater than 100%.

Examples

• To write $225\%$ as a decimal and fraction, divide by 100: $225\% = \frac{225}{100} = 2.25$. As a mixed number, this is $2\frac{1}{4}$ or $\frac{9}{4}$.
• To write the fraction $\frac{8}{5}$ as a percent, first convert it to a decimal: $\frac{8}{5} = 1.6$. Then, multiply by 100: $1.6 \times 100 = 160\%$.

Explanation

Percents greater than 100% are used when comparing a larger quantity (the part) to a smaller one (the whole). This means you have more than the original amount. To convert a percent greater than 100% to a decimal or fraction, you divide by 100, which results in a value greater than 1. Conversely, to convert a decimal greater than 1 or a fraction greater than 1 to a percent, you multiply by 100.

Property

A $10 \times 10$ grid represents $100\%$, or $1$ whole. To model a percent greater than $100\%$, you must use more than one $10 \times 10$ grid:

• Shade one or more entire grids to represent the multiples of $100\%$.
• Shade a portion of an additional grid to represent the remaining percent.

Examples