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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

#### 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.

- Introduction to percents
- Finding percents of numbers
- Percents from fractions (with diagrams)
- Converting between percents and fractions (without diagrams)
- Converting decimals to percents
- Converting percents to decimals
- Equivalent representations of percent problems
- Relate fractions, decimals, and percents
- Percent word problems
- Percent word problems 2
- Discount, tax, markup, and commission word problems

# 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:

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