Once you have done a calculation, with or without the aid of a calculator, it is important that you pause for a moment to check your calculation.

You need to ask yourself some questions.

1. Have I done the right calculation in the right order?

2. Have I given due consideration to units of measurement?

4. Did I make a rough estimate to act as a check?

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1 Measurement of a ceiling gives a length of 6.28 m and a width of 3.91 m.

• (a) Make a rough estimate of the area of the ceiling (the length times the width).

• (b) If one lit
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Approximations are most useful when it comes to making rough estimates â€“ like adding up a bill quickly to see if it is about right or checking a calcul
Author(s): The Open University

You can use the same procedure for numbers less than one.

## Example 4

In scientific work people deal with very small units of measurement. Suppose you read that the spacing between adjacent atoms in a solid was 0.000Â 002Â 456Â 84 metres. You could make the number more memorable by using two sign
Author(s): The Open University

1 Round 2098Â 765

• (a) to 1 s.f.

• (b) to 2 s.f.

• (c) to 3 s.f.

• (d) to 4 s.f.

## AnAuthor(s): The Open UniversityLicense informationRelated contentExcept for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Sometimes it doesnâ€™t make sense to round to a specific number of decimal places. If, say, you were calculating the cost of fencing at Â£10.65 per metre, for a garden boundary, the length of which had been given to you as 185 feet, then you would want to multiply 10.65 Ã— 185 Ã— 0.3048. (Conversion of feet to metres was given in Example 2.)
Author(s): The Open University

1 Round a measurement of 1.059 metres:

• (a) to the nearest whole number of metres;

• (b) to two decimal places;

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Using a calculator often gives a long string of digits. For example, 1 Ã· 3 might give .333333333. But very often, for practical purposes, this level o
Author(s): The Open University

1 Round the numbers below:

• (a) to the nearest 10.

• (b) to the nearest 100.

• (c) to the nearest 1000.

Â Â 325 089,Â Â 45 982,Â Â 11 985
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Numbers are often approximated to make them easier to handle, but sometimes it doesnâ€™t help very much to round to the nearest 10 or the nearest 100 if the number is very large. For example, suppose the monthly balance of payments deficit was actually Â£24Â 695Â 481. Rounded to the nearest 10, it's Â£24Â 695Â 480; and to the nearest 100, it's Â£24Â 695Â 500. But Â£24Â 695Â 500 is still a complicated number to deal with in your head. That's why it was rounded to Â£25 000 000 in the newspaper
Author(s): The Open University

The blouse in the figure above was Â£19 and you may well have thought of it as roughly Â£20. In this case you would be rounding to the nearest ten (pounds).

The rule for rounding to the nearest hundred can be adapted easily to rounding to the nearest ten. Instead of looking at the tens digit look at the units digit.

So Â£23 is rounded down (to Â£20) and Â£36 is rounded up (to Â£40).

Author(s): The Open University

You will probably think to yourself that the coat shown costs about Â£300. Â£290 is considerably closer to Â£300 than it is to Â£200, so Â£300 is a reasonable approximation. In this case, 290 has been rounded up to 300. Similarly, 208 would be rounded down to 200 because it is closer to 200 than it is to 300. Both numbers have been rounded to the nearest hundred pounds.

When rounding to the nearest hundred, anything below fifty rounds down. So 248 rounds to 200. Anything o
Author(s): The Open University

Author(s): The Open University

By the end of this unit you should be able to:

• round a given whole number to the nearest 10, 100, 1000 and so on;

• round a decimal number to a given number of decimal places or significant figures;

• use rounded numbers to find rough estimates for calculations;

• use a calculator for decimal calculations involving +, âˆ’, Ã— and Ã·, giving your answer to a specified accuracy (e.g. decimal places or significant figures) and checking your an
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For many calculations you use a calculator. The main aim of this unit is to help you to do this in a sensible and fruitful way. Using a calculation to solve a problem involves four main stages:

• Stage 1: working out what calculation you want to do;

• Stage 2: working out roughly what size of answer to expect from your calculation;

• Stage 3: carrying out the calculation;

• Stage 4: interpreting the answer â€“ Doe
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The content acknowledged below is Proprietary (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following sources for permission to reproduce material in this Unit:

Author(s): The Open University

This Unit has looked at a variety of ways of comparing prices, and the construction of a price index. Important statistical ideas that contributed to this included mean, weighted mean and median, as well as the general notion of an index.

You now know quite a lot about the CPI, the RPI, and price indices in general, and so you should be able to explain what politicians and journalists really mean when they make sweeping statements about inflation and the cost of living. In the course of
Author(s): The Open University

This final subsection is an overview of the various modes of mathematical communication used so far, like words, tables and graphs, and diagrams. You may have a preference for one over the others as a way of presenting ideas and of receiving information. However, they can all aid your understanding and communication of different mathematical ideas. So you need to develop your skills in using and interpreting all of them.

Look back at Author(s): The Open University

A common criticism of many children's and some adults' drawings is that certain parts are not â€˜in proportionâ€™. That means that they are either too big or too small in relation to the rest of the masterpiece. â€˜In proportionâ€™ means being in the same ratio. Imagine that you have drawn a picture of the front of your house, reducing it in scale to one twentieth of its size.

Author(s): The Open University

It is easy to distinguish children from adults. For one thing, children are usually much smaller. But how are we able to tell them apart from a drawing alone? Have a look at the two outline drawings. Which one do you think represents the child and which the adult?

Author(s): The Open University