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# Outline

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

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:

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: