Decimals and percentages
Audio for slide 1 (mp3 |6|KB)
From fractions to decimals
The fraction bar is like a division sign. For example, 1/2 is another way of saying: 1÷ 2.
If you do this on your calculator, you will find that it equals 0.5. That is: 1÷ 2 = 0.5
To put it another way, 0.5 is the decimal equivalent of 1/2.
Audio for slide 2 (mp3 |6|KB)
That is, if 1/2 equals 0.5, then 0.5 times 2 should equal 1.
You can check this on a calculator to prove it to yourself.
Audio for slide 3 (mp3 |6|KB)
Again, you can check this on a calculator, and double-check it in reverse.
Audio for slide 4 (mp3 |6|KB)
From fractions to percentages
A percentage is simply another way of writing a fraction which has a denominator of 100. Per cent means 'per 100', or 'for every 100'.
For example: 50% equals 50/100, which can be reduced to 1/2.
So if 50% is the same thing as 1/2, then 50% x 2 should equal 100. And indeed it does!
Audio for slide 5 (mp3 |6|KB)
This means that 10% x 10 = 100%
Audio for slide 6 (mp3 |6|KB)
Decimals and percentages
Notice that percentages and decimals are basically the same thing. The only difference is: a percentage is a proportion of 100, and a decimal is a proportion of 1.
Audio for slide 7 (mp3 |6|KB)
Learning activity
Audio 8 (mp3 |6|KB)1. Complete the table below by entering the correct numbers in the cells. When you've finished, click on the 'Check your answers' button to see how you went.
| Fractions to be converted | Value | |
|---|---|---|
| 1/100 to a decimal | 0.01 | |
| 1/20 to a decimal | 0.05 | |
| 1/10 to a decimal | 0.1 | |
| 1/8 to a decimal | 0.125 | |
| 1/5 to a decimal | 0.2 | |
| 1/4 to a decimal | 0.25 | |
| 1/2 to a decimal | 0.5 | |
| 1 to a decimal | 1 | |
| 1/100 as a percentage | 1 | % |
| 1/20 as a percentage | 5 | % |
| 1/10 as a percentage | 10 | % |
| 1/8 as a percentage | 12.5 | % |
| 1/5 as a percentage | 20 | % |
| 1/4 as a percentage | 25 | % |
| 1/2 as a percentage | 50 | % |
| 1 as a percentage | 100 | % |
2. Let's say you have 15 litres of paint, and you're going to apply it with a spray gun. The manufacturer's advice is to add 10% thinners to the paint to improve the flow. How many litres of thinners should you add?
| How many litres of thinners should you add? | 1.5 | litres |
3. If you earned $800 per week and paid 30% in tax, how much tax would you pay each week?
| Taxed paid each week is | 240 | $ |