Percentage
A percentage, or percent, is a number or a ratio that represents a part (or fraction) of 100. The term "percent" comes from the Latin "per centum" which literally means "by a hundred." It is typically denoted using a % sign; "fifty percent" is written as 50%, and means 50 out of 100 of whatever is being measured.
A percent is a dimensionless number, meaning that it has no units of measurement, since it represents a part of whatever whole is being measured. Below is a visual representation of some common percentages using a 10 x 10 array of 100 squares.
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Since there are 100 squares in each of the arrays above, 20% is represented by 20/100 squares, 50% is represented by 50/100 squares, and 75% is represented by 75/100 squares.
Percentages as decimals and fractions
Percentages can also be expressed as decimals and fractions; each is just a different way of representing a part of a whole.
As a fraction
To express a percentage as a fraction, write the % value as the numerator of a fraction with a denominator of 100, then simplify the result if possible.
Examples
Express the following percentages as fractions: 10%, 36%, 83%
1. 10%:
2. 36%:
3. 83%:
As a decimal
To express a percent as a decimal, move the decimal point two places to the left. This works because, in the decimal numeral system, each place represents the subsequent power of 10. Moving a decimal point right is the equivalent of multiplying by 10, and moving a decimal point left is the equivalent of dividing by 10. Since a percentage can be represented as a fraction out of 100, any percentage can be converted to a decimal by dividing by 100 (or shifting the decimal point two places to the left).
Examples
Convert the following percentages to decimals: 10%, 36%, 83%.
1. 10%:
2. 36%:
3. 83%:
Percentages in everyday life
In addition to being used throughout math and science, percentages are used in many aspects of everyday life, such as discounts when shopping, taxes, interest rates, statistics, food labels, and much more. As such, it is important to have a good understanding of percentages to enable you to perform the various percentage calculations you may need in your studies as well as in life. Below are a few such examples.
Sales tax
Sales tax is a tax on certain goods and services. For example, given a sales tax of 8.25%, you would have to pay an additional 8.25% of the price of the goods you purchase.
Example
If there is a sales tax of 8.25%, what is the total amount you will pay for goods that cost $12?
This can be done in a number of different ways using either fractions or decimals. 8.25% is equivalent to 8.25/100, or 0.0825. Multiplying either the fraction or decimal by 12 tells us what 8.25% of 12 is:
0.0825 × 12 = 0.99
This means that you would have to pay an additional 99 cents on top of the $12, for a total of $12.99. We also could've multiplied 12 by 1.0825 to get the same result.
Discounts
Understanding percentages allows us to calculate how much we will save when purchasing discounted things.
Example
A shirt originally priced at $15 is discounted 20%. How much money will you save?
20% of $15 can be calculated by multiplying 15 by 0.20 or 20/100.
Therefore, a 20% discount results in $3 of savings.
There are many other different types of percentage calculations. These are just a few examples to demonstrate how they can be useful in everyday life.