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In order to understand the information on this page, it can be helpful to already know:


Outline

PercentGrid

This 10x10 grid has 100 squares so each represents 1%
64 of the 100 squares, or 64% of the overall area, is shaded.

Percent means "for every 100" and is denoted by the % symbol. The symbol is derived from the diagonal line of a fraction and the two zeros of 100.

In practical terms, a percentage is a multiple of $ \frac{1}{100} $ so:

64% is $ 64 \times \frac{1}{100} $ or $ \frac{64}{100} $.





Worked Examples

Equivalent values

Convert Percent to Fraction

Sample question:

"Convert 23% to a fraction"

Solution:

Remember that percent is the number of hundredths so replace the % symbol with "$ \times \frac{1}{100} $" then simplify.
$ 23% = 23 \times \frac{1}{100} = \frac{23}{100} $

Convert Percent to Decimal

Sample question:

"Convert 23% to a decimal"

Solution:

To convert to a decimal, use the decimal equivalent of $ \frac{1}{100}=0.01 $
$ 23% = 23 \times \frac{1}{100} = 23 \times 0.01 = 0.23 $

Convert Fraction to Percent

Sample question:

Express $ \frac{3}{5} $ as a percent

Solution:

First, convert the fraction to have a denominator of 100 then rearrange as a multiple of $ \frac{1}{100} $
$ \frac{3}{5}=\frac{60}{100}=60\times\frac{1}{100}=60% $

Convert Decimal to Percent

Sample question:

Express 0.458 as a percent

Solution:

Start by rearranging to a multiple of 0.01 then continue as you would for a fraction.
$ 0.458=45.8 \times 0.01 = 45.8 \times \frac{1}{100}=45.8% $

Finding a percentage of a value

Sample question:

What is 23% of $400?

Solution:

First, convert the 23% to a fraction or decimal (methods shown earlier) then multiply the result by $400.
$ 23% \ of \ $400 = 0.23 \times $400 = $92 $

Practice

You can practice skills in percent using the following references:

Khan Academy

Make sure you are logged in to Khan Academy when doing these exercises so your practice is recorded.

Application

Percentages are often used in financial applications where a proportion calculation is required. These include:

  • Discounts (percentage of original price)
  • Profit margin (percentage of sale price)
  • Tips (percentage of total bill)
  • Loan or Deposit interest (percentage of balance)

Next Steps

Comfortable with percents? Check out the follow-on mathematics you can now do: