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Competencies covered

MSFGN2001: Make measurements and calculations

Decimals and percentages

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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.

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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.

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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.

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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!

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Audio for slide 5 (mp3 |6|KB)
Here's another example: 10% = 10/100 = 1/10

This means that 10% x 10 = 100%

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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.

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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.

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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.

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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?

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How many litres of thinners should you add? 1.5litres
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?

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Taxed paid each week is240$