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)
It's easy to confirm this answer by doing the calculation in reverse.

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)
In the same way, the fraction 1/4 is equivalent to the decimal 0.25.

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)
Here's another example: 10% = 10/100 = 1/10

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)
Therefore: to change a decimal to a percentage, multiply by 100, and to change a percentage to a decimal, divide by 100.  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 convertedValue
1/100 to a decimal0.01
1/20 to a decimal0.05
1/10 to a decimal0.1
1/8 to a decimal0.125
1/5 to a decimal0.2
1/4 to a decimal0.25
1/2 to a decimal0.5
1 to a decimal1
1/100 as a percentage1%
1/20 as a percentage5%
1/10 as a percentage10%
1/8 as a percentage12.5%
1/5 as a percentage20%
1/4 as a percentage25%
1/2 as a percentage50%
1 as a percentage100%
Audio 9 (mp3 |6|KB)

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
Audio 10 (mp3 |6|KB)

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 \$ Go to The metric system