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1.2.3 Working with percentages

Table 1 used percentages, rather than actual numbers, to compare the number of people using the internet for each purpose. Numbers are expressed as if they are 'out of a hundred' when using percentages, which makes it easier to compare different values. You can recognise percentages by the % symbol which you can see at the top of the right-hand column of Table 1.

As you can see from halfway down the table, 50% of the people who had used the internet in the previous 3 months used it for buying or ordering things. (They may also have used it for other purposes.)

How many people is that? Obviously, that would depend on the total number of people. For argument's sake, we will say that 100 people in total had used the internet in the previous three months. That's relatively easy to work out: 50% of 100 is 50 out of 100, which is 50.

What if there were 200 people who had used the internet and 130 of them said that they used it for general browsing? This figure of 130 can be expressed as a percentage of 200.

Firstly, 130 is converted to a fraction of 200:

Then the fraction is multiplied by 100:

Which is:

(i.e. 13000 divided by 200)

which gives a result of 65.

If you wish, you can work this out using your Windows calculator; enter '130 / 200×100 ='.

We can now say that 65% of the 200 people who had used the internet said they used it for general browsing.

Activity 5 (self-assessment)

Try the following three percentage calculations.

  1. In a survey involving 700 people, 420 people said that they use the Internet for general browsing. What percentage is this?

  2. In a group of 320 students, 120 said that they mainly use a laptop in their studies rather than a desktop computer. What percentage of students use a laptop?

  3. On a production line for computer monitors, 3 out of 750 monitors are faulty. What percentage of monitors are faulty?

Answer

  1. 420 / 700×100=60

    So 60% of the people surveyed use the internet for general browsing.

  2. 120 / 320×100=37.5

    So 37.5% of the students use a laptop.

  3. 3 / 750×100=0.4

    So 0.4% of the monitors are faulty.

All the data in Table 1 is expressed in percentage form, but, if we know how many people were interviewed in the survey, we can work back from the percentage to find the actual number. Suppose 1700 people are interviewed in a survey and 56% of them say they have used the internet in the last 3 months. How many people does 56% represent? We can find out as follows.

First the percentage is expressed as a fraction of 100:

The fraction is then multiplied by the total number of people in the survey:

Using the Windows calculator, I enter '56 / 100×1700 ='. The result is 952. This means that 952 of the 1700 people surveyed used the internet in the last three months.

Now suppose that, according to the survey, of those 952 people who used the internet in the last three months, 85% used it for email. How many people out of the 952 used the internet for email? We can calculate the number by finding 85% of 952.

With the Windows calculator I enter '85 / 100×952 ='. The answer is 809.2 people, but common sense suggests that the answer ought to be 809.

T175_7

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