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Succeed with maths: part 1

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# 2 Rounding

The world population in April 2021 was estimated to be 7.86 billion. That is not an exact value but it does give you an indication of the world’s population at the time. This is an example of a rounded or estimated number.

In newspapers and elsewhere, numbers are often rounded so that people can get a rough idea of the size, without getting lost in details. You may use rounding yourself, such as prices in a supermarket (£2.99 is about £3) or distances (18.2 miles is about 20 miles).

Using approximate values is also useful if you want to get a rough idea of an answer before you get out scrap paper or a calculator. This estimation acts as a check on your calculation and may help you to catch any errors you may have.

The general rules for rounding are:

• Locate the place value to be rounded.
• Look at the next digit to the right.
• If that digit is a 5 or greater, ‘round up’ the previous place value digit – which means increase it by one.
• If that digit is a 4 or less, leave the previous place value digit unchanged.
• Replace all digits after the place value digit with 0, but only if these are to the left of the decimal point.

This last rule may be a little harder to understand, so here’s an example.

If you are rounding 5423 to the nearest one hundred this would be 5400 – the tens and units places being replaced by zeros.

With decimals we often refer to the number of decimal places to round to rather than a digit’s place value. So, instead of asking you to round to the nearest tenth, you might see instructions to ‘round to 1 decimal place’ (1 d.p.). The decimal places are numbered consecutively from the right of the decimal point. So, 1.54 has 2 decimal places, and 34.8942 has 4 decimal places.

Whether you are rounding using place value or decimal places, the general rules remain the same.

Before you have a look at some examples, you might like to view this video on rounding.

Interactive feature not available in single page view (see it in standard view).

Here are a few more examples to have a look at before you have a go yourself.

Imagine you want to round the world population figure of 7.86 billion to the nearest billion. The place value that you want to round in this case is the units as these represent the billions, which is a 7. The next number to the right of this is a 8, which is 5 or more, so you need to round up and the 7 becomes an 8.

So 7.86 billion rounded to the nearest billion is 8 billion.

Now suppose you want to round 1.72 to 1 decimal place. The 7 is in the first decimal place and to the right of this is a 2. This is 4 or less, so the 7 stays as it is.

So 1.72 rounded to 1 decimal place is 1.7. Now it’s your turn.

## Activity 2 Rounding

Timing: Allow approximately 5 minutes

Round each of the following numbers as stated.

(a) Round 126.43 to the nearest tenth.

• Locate the place value to be rounded – in this case, the number 4.
• Look at the next digit to the right – in this case, it’s 3.
• 3 is less than 5, so you round down, and the answer is 126.4.

(b) Round 0.015474 to the nearest thousandth.

• Locate the place value to be rounded – in this case, the number 5.
• Look at the next digit to the right – in this case, it’s 4.
• Because 4 is less than 5, you round down, and the answer is 0.015.

(c) Round 1.5673 to 2 decimal places (2 d.p.).

• Locate the decimal place to be rounded – in this case the number is 6.
• Look at the next digit to the right – in this case, it’s 7.
• Because 7 is greater than 5, you round up, and the answer is 1.57.

Now complete Activity 3.

## Activity 3 How much is it?

Timing: Allow approximately 10 minutes

Suppose you want to buy a new pick-up truck. When you visit the dealership’s website, it says the cost of the vehicle you are looking at is £19 748. When you call the dealership on Thursday, the sales representative, Joe, tells you the cost is £19 750. However, the next day another sales representative, Tina, informs you that the vehicle costs £19 700. Why did the quote you were given on the cost of the pick-up truck change?

Hint: Round the website cost to the nearest £10. Then round the website cost to the nearest £100.