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Try some yourself

Activity 22

Carry out the following calculations, without using a calculator.

  • (a) A million pound lottery prize minus a three hundred pound administrative charge.


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3.1 Arithmetic with whole numbers

When you are adding or subtracting whole numbers, an important thing to keep in mind is the place value of the figures. It is often a good idea to set out the numbers in columns before doing the arithmetic.

Example 11

  • (a) There are 4
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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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2.11 Further exercises

Exercise 28

Let z1 = 2 + 3i and z2 = 1 − 4i. Find z1 + z2, z1z2, z1z
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2.10 The complex exponential function

Consider the real exponential function f (x) = ex (that is, f (x) = exp x). We now extend the definition of this function to define a function f(z) = ez whose domain and codomain are Author(s): The Open University

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2.2 The complex plane

Just as there is a one-one correspondence between the real numbers and the points on the real line, so there is a one-one correspondence between the complex numbers and the points in the plane. This correspondence is given by

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Acknowledgements

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

Course image: Stuart Rankin in Flickr made available under Creative Commons Attribution-NonCommercial 2.0 Licence.

All materials included in this course are
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Try some yourself

Question 1

Find the area of each of these shapes.

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Environment: journeys through a changing world
Genetically, mountain gorillas are amongst our closest living relatives, and also one of the world's most endangered species. Half the world's remaining population survive in the forests of Uganda. This album explores the challenges facing conservationists at Bwindi Impenetrable National Park. Known for its exceptional biodiversity, the Park became a major tourist destination when it opened for gorilla tourism in 1993. The problem is, because the Park lies in the heart of one of the most densely
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Water in Ethiopia
In Ethiopia, 65% of people don’t have access to clean drinking water. In this album we take a glimpse at the struggles Ethiopians go through each day, just to survive. We look closely at the different methods used to improve the quality of life in the rural highlands as well as the conflict between neighbouring farming villages attempting to share the same water supply. This material forms part of the course U116 Environment: journeys through a changing world.Author(s): The OpenLearn team

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Environmental responsibility
Complex questions of environmental responsibility are increasingly raised in times of change and uncertainty. The tracks on this album illustrate the need for nurturing a fresh sense of care for our environment as well as more appropriate forms of accountability. We demonstrate the necessity of addressing issues of entitlements, rights, obligations and duties if we are to critically and carefully shape our values in doing environmental responsibility and being environmentally responsible. This m
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Enacting European Citizenship (ENACT)
The term 'European citizenship' triggers an immediate association with the European Union, its member states, and people who are citizens of those states. This free course, Enacting European Citizenship (ENACT), develops another way of thinking about European citizenship whereby European citizenship need not be granted by the state, limited to the territory within the EU borders or acted out by people who are already citizens. Author(s): Creator not set

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The frozen planet
This free course is a general introduction to the frozen planet, including the temperature in the polar regions; the energy from the Sun and the seasons; reading and understanding graphs and maps; and how the Arctic and Antarctic regions are defined. First published on Wed, 06 Dec 2017 as Author(s): Creator not set

Neighbourhood nature
There is a fascinating world of nature all around us which we can see if we know how to look for it. Wherever you live, be it in a city or the countryside, you will find areas that support a range of wildlife. This free course, Neighbourhood nature, will provide you with basic scientific and observational skills so that you can go into your local neighbourhood to discover the animals and plants in open spaces. You will learn how to observe, identify and record the wildlife around you, building u
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1.6 The human impact on the atmosphere: the coming of the industrial age

There is no doubt that CO2 is accumulating in the atmosphere. The record from Mauna Loa charts a continuing rise in CO2 concentration since measurements began in 1958, when the level was 315 ppm; the value had reached about 370 ppm by the end of the 20th century, and hit more than 378 ppm in 2004. Important as changes in atmospheric CO2 undoubtedly are (see below), we need to be aware that this is not the whole story of human-induced greenhouse forcing. In par
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1.3.2 The fate of incoming solar radiation

SAQ 9

Look back at Figure 7. In this schematic representation, what is the fate of incoming solar radiation?

Answer

It is either reflected back to spa
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1.3.1 The vertical 'structure' of the atmosphere

The atmosphere is not a simple, uniform slab of absorbing material. On the contrary, it gets progressively 'thinner' or less dense with increasing altitude (height above mean sea level); i.e. the total number of molecules in a given volume of air is lower, and so is the pressure. About 80% of the total mass of the atmosphere is within some 10 km of the surface; 99.9% lies below 50 km.

The important corollary is that the key greenhouse gas molecules (H2O and CO2
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Introduction

This course explores the topic of climate change and global warming. We will begin by exploring how the Earth's global mean surface temperature is determined through a global “balancing act” of the rate of energy that comes from the Sun and the rate at which the planet returns that energy into space. We will also discuss the natural greenhouse effect, and how this contributes to a balanced global climate. We will then go on to consider the human impact on the atmosphere, including the imp
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2.1 Dealing with change in what matters: ethics, policy and action

Much of what has been covered so far in this unit deals with the individual human capacity to frame nature as a means for enabling environmental responsibility. But what are the implications of this for actually doing something about policy design and action to improve matters? Framing the natural world is an inevitable human endeavour that we all carry out, whether consciously or subconsciously, as part of our interaction with human and non-human nature. For example, each of the tools listed
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