Percentage

Percent can be expressed as a fraction (with a denominator of 100) or a decimal. For example, 29% = $\genfrac{}{}{1px}{}{29}{\mathrm{100}}$ = 0.29

Percents are often used to compare fractions with equal denominators of 100. To convert a percent to a fraction, drop the percent sign and divide the number by 100. For example, 80% = $\genfrac{}{}{1px}{}{80}{\mathrm{100}}$ = $\genfrac{}{}{1px}{}{4}{5}$ and 125% = $\genfrac{}{}{1px}{}{125}{\mathrm{100}}$ = $\genfrac{}{}{1px}{}{5}{4}$ = 1$\genfrac{}{}{1px}{}{1}{4}$

As a more complicated example, consider the following: To convert a fraction to a percent, multiply the number by 100 and insert the percent sign. For example,

To convert a percent to a decimal, drop the percent sign and divide the number by 100 (i.e., move the decimal point two places to the left, inserting zeros to the left if necessary). For example, 13% = 0.13 and 2% = 0.02

To convert a decimal to a percent, multiply the decimal by 100 (i.e., move the decimal point two places to the right) and insert the percent sign.

Example

0.2576 = 25.76% and 0.002 = 0.2% To find a certain percent of a number, multiply the number by the percent expressed as a fraction or decimal. For example, to find 45% of 900, two possible ways are as follows. Changing the percent to fraction gives 45% = $\genfrac{}{}{1px}{}{45}{\mathrm{100}}$ = $\genfrac{}{}{1px}{}{9}{\mathrm{20}}$. So, $\genfrac{}{}{1px}{}{9}{\mathrm{20}}$ × 900 = 405.

Alternatively, changing percent to decimal gives 45% = $\genfrac{}{}{1px}{}{45}{\mathrm{100}}$ = 0.45. So, 0.45 x 900 = 405. The following fraction and decimal equivalents of percents are worth noting:

Percent Change

Percent change (increase or decrease) from an original value to a new value frequently occurs. To find the percent change, first, find the amount of the change, then divide this amount by the original value, and finally express this quotient as a percent.

Example

If the price of an item changes from $32 to $40, the amount of the increase is $(40 − 32) = $8 and the percent increase is $\genfrac{}{}{1px}{}{8}{\mathrm{32}}$ = $\genfrac{}{}{1px}{}{1}{4}$ = 0.25 = 25%.

On the other hand, if the price of the item changes from $40 to $32, the amount of the decrease is $(40 − 32) = $8 and the percent decrease is $\genfrac{}{}{1px}{}{8}{\mathrm{40}}$ = $\genfrac{}{}{1px}{}{1}{5}$ = 0.2 = 20%.

Interestingly, the percent increase from 32 to 40 is different from the percent decrease from 40 to 32.