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
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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
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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

This subsection looks at two ways of finding an â€˜averageâ€™. The first produces the mean, which is what was originally meant by â€˜averageâ€™, and what most people think of when they talk about an average. The second gives the median, which might more accurately be described as a â€˜typicalâ€™ or middle value. They will be illustrated using the following batch of heights.

The heights in metres (measured to the nearest centimetre) of a group of seven people are as follows
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This subsection discusses using a typical basket of goods to analyse price changes over time. However, what is meant by â€˜typicalâ€™?

Think back to the last time you went shopping. What did you buy? The electric light bulbs that you have just stocked up on are unlikely to be in your shopping basket next week, whereas milk may well be there every week. And there may be itemsâ€”a new toothbrush for exampleâ€”that you buy from time to time, but not this week.

To monitor price change
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Hopefully, thinking about how your solution to a mathematical problem might be marked, will help you to produce better solutions for yourself, as well as for somebody else. Now try the quizÂ  and see if there are any areas you need to work on.

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Learning from the marking of the previous questions, write out a good solution to the following problem.

## Example 18: Making a lawn

Suppose you have some friends who are planning to put a new lawn in their garden. The lawn is to be 12 m by 14 m and they have a choice of either laying turf or sow
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Write out your own solution to the following problem.

## Example 17: St Ives

As I was going to St Ives

I met a man with seven wives.

Kits,
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1 You are planning to paint three rooms with total wall areas of 56, 38 and 40 square metres, using paint that comes in tins which claim to cover 15 square metres per tin. How many tins will you need for each room? And how many in total?

<
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Formulas are important because they describe general relationships, rather than specific numerical ones. For example, the tins of paint formula applies to every wall. To use such a formula you need to substitute specific values for the general terms, as the following examples show.

## Example 8

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First you need some data about corresponding temperatures on each scale. In the case of Celsius and Fahrenheit, there are two fixed points of reference: the freezing and boiling points of water. On the Celsius scale, the freezing point is defined to be 0Â°C; on the Fahrenheit scale, the freezing point is 32Â°F. So if you plot degrees Celsius on the horizontal axis and degrees Fahrenheit on the vertical axis of a graph, the freezing point of water is represented by a point with the coordinates
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Discount can be calculated in the same way as an increase by a percentage. For example, Â£8 with 15% discount means you actually pay

Â Â Â£8 less (15% of Â£8)

Â Â 15% of 8 = Ã— 8 = Author(s): The Open University

Peace of Paris (1783)
Video accompanied with text. "After Yorktown, the citizens of Britain tired of the war in the American colonies. They were also greatly in debt and had suffered immense losses in India, the West Indies, Asia, and Africa. In February 1782, the House of Commons voted against continuing the war, and in March 1782 Lord North resigned, ending the rule of King George III. The new ministry included old friends of the Americans and was headed by Lord Rockingham who was prepared to negotiate a peace sett
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Course image: Davide D'Amico in Flickr made available under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence.

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

Grateful acknowledgement is
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Real Brazilian Conversations #36 â€“ Avisos Importantes e Carnaval
Hello guys, Guilherme here. After a little break, weâ€™re back again! Today I talk about an important cultural event in Brazil, the Carnival! Thre is something I need you to know about RLP, listen to...

Check out our website, reallylearnportuguese.com and find out more how we can help you to improve your Portuguese language skills!

Masayoshi Son is betting \$100bn on the world's most exciting technology startups. Win or lose, his Vision Fund is shaking up the tech industry and those that invest in it. Plus, the Pulitzer-prize winning playwright David Mamet on his new comedy inspired by Harvey Weinstein. And are smartphones the key to escaping poverty?

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## Study another free course

There are more thanÂ 800 coursesÂ on OpenLearnÂ for you to choose from on a range of subjects.Â

Find out more
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Another way to tackle unfamiliar words is to start a â€˜concept cardâ€™ system, using index cards. When you meet a word which seems important, take a new card and write the word at the top, followed by any useful information you have found. File the cards alphabetically and add details as you come across new information. (It is worth getting an index card box anyway, then you can try out various ways of using it to organise your studies.)

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This key skill has used a three-stage framework for developing your skills. By developing a strategy, monitoring your progress and evaluating your overall approach, you take an active role in your own learning. But learning does not necessarily follow a path of steady improvement, it involves change: revisiting ideas, seeing things from different perspectives, tackling things in different ways.

You are unlikely to be able to complete your work by working through it from beginning to end
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Digital Library Object - Graphics-oriented battlefield tracking systems: U.S. Army and Air Force int