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2.3 Measuring mass

The basic SI unit for mass is the kilogram, symbol kg

The tonne (t) which is equivalent to 1000 kg and is a metric unit is often used alongside the SI units.

The animation below illustrates how to convert between the most commonly used units of mass, the metric tonnne (t); the kilogram (kg); the gram (g); the milligram (mg) and the microgram (μg).

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Units in action

Example 7

Imagine a friend is planning a new kitchen in her house. In the kitchen showroom she noticed that the measurements of most of the kitchen units were given in millimetres. One worktop, for instance, is 575 mm deep. What units should she use to measure the large room in the house where the ne
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Try some yourself

1 What is 370.76 grams in kilograms? There are 1000 grams in a kilogram.

Answer

370.76 ÷ 1000 = 0.370 76.

So 370.76 g = 0.370 76 kg.


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1.5.1 Introduction

Quantities can be smaller than one (such as 0.5 kg) or take values between whole numbers (such as a height of 1.65 metres). Numbers smaller than one are expressed as decimals or as fractions. Decimals are often easier to work with (especially when using a calculator). Decimals are explained in this section, and fractions following that (Author(s): The Open University

1.2.1 Introduction

Whole numbers arise from counting: for example the number of sheep in a field or the number of votes in an election.

Our everyday number system is the decimal system, where the position of a digit within the number determines whether it represents units, tens, hundreds, thousands etc.


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5.1: What are the CPI and RPI?

The Consumer Prices Index (CPI) and the Retail Prices Index (RPI) are published each month by the UK Office for National Statistics. These are the main measures used in the UK to record changes in the level of the prices most people pay for the goods and services they buy. The RPI is intended to reflect the average spending pattern of the great majority of private households. Only two classes of private households are excluded, on the grounds that their spending patterns differ greatly from t
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Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence

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

Except for third party materials and otherwise stated (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 mater
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1.6.3 Don’t jump to conclusions

Time-series graphs are popular with newspapers for suggesting and comparing trends. But showing how a single quantity varies with time is not the same as showing how two quantities vary, and then suggesting a link between them.

Figure 34Author(s): The Open University

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1.5.1 Mathematical graphs: special terms

Mathematicians use some special terms to talk about graphs. Understanding and feeling confident with this graphical language is as much a part of mathematics as doing calculations, or working with formulas. By convention, the horizontal axis of a graph – the one running across the page from left to right – is often called the ‘x-axis’, and the vertical axis – the one running up the page – is called the ‘y-axis’, as in Author(s): The Open University

3.3 Time-series graphs: summing up

So time-series graphs must be read with care. Adopt a questioning attitude when you are faced with a graph. Look carefully at the vertical axis to see just what the range of variation is, and at the horizontal axis to see what time intervals have been chosen. Ask yourself about the significance of this choice – what might be going on between each plotted point?

You might question whether the plotted variation is significant or whether it is the result of expected fluctuations. What ab
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Acknowledgements

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7 Subtracting decimals by lining them up

Subtracting whole numbers such as 52 from 375 is fairly straightforward. Subtracting decimal numbers such as 6.892 from 223.6 uses the same process but with one extra step – you have to line the decimal points up first.

Rather than arranging your two numbers so that they line up on the right-hand side, you need to line up the decimal points, regardless of how many numbers there are after the decimal point. In the example below, the top number has one number after the decimal point. It
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10 Dividing by big numbers – long division

In the previous sections you saw how to divide a big number by a small number up to 10. Things get harder if you want to do a division where both the numbers are big. This kind of calculation is called long division, probably because you write the steps of the calculation out on paper in a long sequence.

The principle of doing long division is the same as when you divide by a number up to 10. The only difference is that, because the numbers involved in long division are usually too big
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6 Dividing on paper

If the numbers you want to divide are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper. In the example below, click on each step in turn to see how to divide 126 by 6.

Active content not displayed. This content requires JavaScript to be enabled, and a
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4.5: The mode

The USA workforce data in Table 2 were usefully summarised in Figure 6, w
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Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

The content acknowledged below is Proprietary and used under licence (not subject to Creative Commons licence). See Terms and Conditions.

Unit image

© Keith Glover Photography

All other material contained within this unit originated at the Open University.

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5 Approaches to problem solving

You should not expect always to be able to read a problem and then just write down the answer. When you are faced with a written mathematical question or problem to solve, read it carefully. It is important that you get to grips with the question in two ways: first, that you absorb the information given; and second, that you find out what the question is really asking. Your solution will link the two. This method can be summarised by the following questions.

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2.2.1 Try some yourself

1 Here is a poor example of mathematical writing, although the final answer is correct. Rewrite it, correcting the layout and the mathematical punctuation.

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3.6.1 Try some yourself

1 The population of a village is 5481. Round this:

  • (a) to the nearest thousand people;

  • (b) to the nearest hundred people.

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