# 2 Percentages

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# Introduction

Review the Year 7 syllabus on Percentages, specifically:

The difference from Year 7 is that there may be decimals given in the percentage, or more complicated percentages to make it more challenging.

In addition:

- You need to know how to convert a percentage with a fraction into a fraction. For example, . To do this, we first convert the 1/4 to a decimal, so the entire percentage becomes 106.25. Thus, this is
- You need to know how to convert a fraction into a percentage with rounding (for 2dp, where “dp” means “decimal places”) For example,

In Year 7, we talked about converting fractions to percentages. The idea of expressing a percentage composition as a percentage, by multiplying by 100% is based on the same principle.

For example, 10/50 as a percentage is

# More than 100%

When a percentage is expressed as a fraction, and that fraction’s numerator (top) is greater than its denominator (bottom), it is “more than 100%”.

For example, , which is greater than 100%.

Percentages more than 100% are useful to know how many times greater something is than another thing.

For example, if Miley Cyrus is 165cm, and I am 182cm, if we calculate , we get 1.103 (rounding off). Therefore, we know that I am 110% her height, or 10% taller than she is.

# Application of Percentages

A large part of maths in year 8 relating to percentages will be about applying percentages, including in:

- Parts of a whole, which relates to a whole table of data given, for example the composition of carbon/nitrogen/oxygen/fluorine is given, and you need to find what percentage of that composition is oxygen.
- Profit, which relates to finding percentage profit (or loss), which is the profit/revenue. The other percentage is your expense
- Commission, which is the percent earned from a sale
- Discount, which is the percent decrease of the price of the item from its original price

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