1 Find the following powers by hand, as estimates for calculator work.

• (a) 107

• (b) 108

• (c) 34

• (d) (2)2
Author(s): The Open University

Given any number, you now know how to find its square. But, given the squared number, how do you find the original number?

## Example 3

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

• evaluate the squares, cubes and other powers of positive and negative numbers with or without your calculator;

• estimate square roots and calculate them using your calculator;

• describe the power notation for expressing numbers;

• use your calculator to find powers of numbers;

• multiply and divide powers of the same number;

• understand and apply negative powers, t
Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and 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:

Example 3 Table: Copyri
Author(s): The Open University

Pie charts are representations that make it easy to compare proportions: in particular, they allow quick identification of very large proportions and very small proportions. They are generally based on large sets of data.

The pie chart below summarises the average weekly expenditure by a sample of families on food and drink. The whole circle represents 100% of the expenditure. The circle is then divided into ‘segments’, and the area of each segment represents a fraction or pe
Author(s): The Open University

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Once you have completed the workbook and exercises return to this page and watch the video below, ‘The arch never sleeps’, which discusses a practical application of some of the ideas in workbook.

Click 'View document' to open the workbook (PDF, 0.8
Author(s): The Open University

There are many websites where you will find useful information on maths and statistics. With all information on the internet you need to make a judgement on its reliability.

Royal Statistical Society Information about the Society, its publications, section and groups. Also covers caree
Author(s): The Open University

Whatever resource you choose to use to find information on the internet, many of the same principles apply. Each source that you use will probably look quite different from the one you tried before, but you'll notice that there are always features that are similar – a box to type your search terms in, for instance, or a clickable help button. Different resources refer to the same functions using different terminology, but the principles behind them are exactly the same. The trick is to chec
Author(s): The Open University

For Iris Marion Young, the responsibility of those in North America and Europe towards distant others does indeed rest with their connections to injustices elsewhere, but it would be a mistake to stretch this line of reasoning too far. Although these connections, whether as a consumer, boardroom executive or shop manager, can establish a line of responsibility, as was claimed in Section 3.1, for Young this is only the starting point and not the end point of our involvement. We do not have to
Author(s): The Open University

On this view, market responsibility looks something like this: if left alone, foreign companies will do what they do best, which is to spot an opportunity in the global marketplace, take advantage of it, and then try to keep the spoils of globalisation to themselves until such time that they are forced by market pressures to share them with the local population in the form of higher wages and other such improvements. Or in Krugman's stinging words:

Author(s): The Open University

In economic terms, green consumerism is typically expressed using measures based on the willingness to pay (WTP) principle. As mentioned above, this takes two main forms: eco-taxation, in which environmental costs are estimated and added to the price of commodities (e.g. vehicles with high carbon emissions); and eco-labelling, in which products are labelled with relevant environmental information, such as is now required by the food industry and governments in many industrialised count
Author(s): The Open University

Evidence suggests that global temperature is beginning to rise. There are several factors that could cause this. Only one is affected by human activity.

Click on 'View document' to view a chart showing the rates of energy gain and loss by the Earth's surface and atmosphere

Unfortunately, halting the disappearance of species cannot be achieved simply by measures such as putting fences around special habitats and asking people not to pick the flowers or disturb the breeding birds. Many species are vanishing because of pollution. You probably have a good understanding of the meaning of this term, but it is variously defined. The Open University has a course on environmental control and public health, in which pollution is defined as the introduction into th
Author(s): The Open University

Fossil and nuclear fuels are often described as non-renewable because supplies are finite and will eventually run out. Renewable fuels are those energy sources that will not run out in the future.

Most renewable energy sources originate from the sun (solar energy), while tidal energy originates from the gravitational pull of the moon, and geothermal energy results from heat trapped below the surface of our planet.

Solar energy can be used directl
Author(s): The Open University

I would like to turn now to the possible consequences of our use of energy for global climate change. Our pattern of energy use relies heavily on burning carbon-based fossil fuels, releasing carbon dioxide which spreads evenly around the globe and builds up slowly in the atmosphere. Carbon dioxide is a greenhouse gas, which means that it has the potential both to warm the atmosphere and to change our global climate. It is not the only greenhouse gas but is the most important of those e
Author(s): The Open University

A central concern of environmental studies is the relationship between technology and our environment: how people use technology to transform materials into forms which can meet our needs and wants. In the process of doing this we inevitably change the environment which provides these materials but which also supports all life.

A few moments ago I went to my fridge and took some milk out to add to a cup of coffee. I used this common example of a modern domestic appliance without a secon
Author(s): The Open University

The international level can be viewed as an arena of politics in its own right and not just as a context for states and other actors. If we think of the international world in this way, how should relations between states, and other actors on the international stage, be constructed? To what extent should those relations be regulated? We can ask whether relations between states, and states' policy making, should be dictated by allegedly universally shared human rights principles, or by other o
Author(s): The Open University

The aftermath of the 2004 Indian Ocean tsunami saw an unprecedented aid effort to assist the affected regions. In the early days after the disaster, pledges of financial assistance from overseas governments were often outstripped by the generosity of their own populaces. This was a case when ordinary people around the world saw and were moved by the tragic circumstances of others far away (Rose, 2006), and they responded with gifts of money and provisions, and even with offers of their own sk
Author(s): The Open University

## Course Team Chair of Production

Gillian Rose, Professor of Cultural Geography

## Course Team Chair of Presentation

Chris Brook, Senior Lecturer in Geography

## External Assessor

Peter Jackson, Professor of Human Geography, University of Sheffield

## Author(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

Global markets for manufactured goods, as opposed to, say, primary commodities such as oil and timber, arose largely in the second half of the twentieth century as trade between countries intensified. The lowering of transport costs and the relative fall in trade barriers enabled firms in one country to compete wit
Author(s): The Open University