# 8.03 Convert between fractions, decimals and percentages

Lesson

## Ideas

Let's review how to write  fractions as percentages  .

### Examples

#### Example 1

Express the fraction \dfrac{5}{25} as a percentage.

Worked Solution
Create a strategy

Find the equivalent fraction that has a denominator of 100.

Apply the idea

To get a denominator of 100, we need to multiply 25 by 4 since 25\times 4=100. But if we multiply the denominator by 4 we must also multiply the numerator by 4.

Idea summary

We can convert any fraction into a percentage by finding its equivalent fraction that has a denominator of 100. After this, we can write the value in the numerator followed by the \% symbol to represent the percentage.

## Convert decimals, fractions and percentages

This video looks at strategies to complete tables of equivalent values for fractions, decimals and percentages.

### Examples

#### Example 2

Convert between percentages, fractions and decimals to complete the table:

Worked Solution
Create a strategy

To convert fractions and decimals to percentages multiply by 100\%. To convert between fractions and decimals use a place value table.

Apply the idea

First we can convert the fraction to a percentage:

The fraction \dfrac{60}{100} means 60 hundredths. So we can write it in a place value table to convert to a decimal:

We can simplify this decimal by writing it as 0.6.

Idea summary

We can convert fractions and decimals to percentages by multiplying by 100\%.

## Percentages and complements

This video looks at how 1 whole is 100\%, and how we can use that knowledge to find complements, that add together to make the whole.

### Examples

#### Example 3

What is the complement of 40\%?

Worked Solution
Create a strategy

Subtract 40\% from 100\%.

Apply the idea

To find the number that makes 100\% when added to 40\%, we can just subtract 40\% from 100\%.

Idea summary

1 whole is 100\%.

If you have a percentage such as 25\%, the complement to that is 75\% because it makes up the whole.

### Outcomes

#### MA3-7NA

compares, orders and calculates with fractions, decimals and percentages