Now look at what happens when the power is negative. What does 10^{âˆ’3} mean? What is the result of the following calculation?

100 Ã· 100 000

What you are actually being asked to find is:

But look at the calculation again. Using the rule for the division

**1** What are the following?

(a) 1

^{0}(b) 0

^{1}(c) 2

^{0}(d) 0

^{2}

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

(a) 10

^{7}(b) 10

^{8}(c) 3

^{4}(d) (

^{âˆ’}2)^{2Author(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

If the gardener in Author(s):

**1** Evaluate the following:

(a) 6

^{2}(b) 0.5

^{2}(c) 1.5

^{2}

## Answer<

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

This unit reminds you about powers of numbers, such as squares and square roots. In particular, powers of 10 are used to express large and small numbers in a convenient form, known as *scientific notation*, which is used by scientific calculators.

This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offer in Author(s):

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

1.1 Understanding scale diagrams

Plans of houses and instructions for assembling shelves, etc., often come in the form of **scale diagrams**. Each length on the diagram represents a length relating to the real house, the real shelves, etc. Often a scale is given on the diagram so that you can see which length on the diagram represents a standard length, such as a metre, on the real object. This length always represents the *same* standard length, wherever it is on the diagram and in whatever direction.

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, â€˜The arch never sleepsâ€™, which discusses a practical application of some of the ideas in workbook.

Click 'View document' to open the workbook (PDF, 0.8

On completion of this unit you should be able to:

convert a vector from geometric form (in terms of magnitude and direction) to component form;

convert a vector from component form to geometric form;

understand the use of bearings to describe direction;

understand the difference between velocity and speed;

find resultant displacements and velocities in geometric form, via the use of components.

Referencing is not only useful as a way of sharing information, but also as a means of ensuring that due credit is given to other peopleâ€™s work. In the electronic information age, it is easy to copy and paste from journal articles and web pages into your own work. But if you do use someone elseâ€™s work, you should acknowledge the source by giving a correct reference.

Taking someone's work and not indicating where you took it from is termed plagiarism and is regarded as an infringemen

*The Two Mile Time Machine*, Princeton, Princeton University Press.

*Nunatsiaq News*, 25 August, p. 11.

The Keeling curve is the plot showing the trend in rising atmospheric CO_{2} concentrations since 1958 recorded at Mauna Loa in Hawaii. The story of atmospheric CO_{2} in the last 50 years is a relentless rise derived from human use of hydrocarbons and, as I write this in 2008, the annual mean concentration is 383 parts per million (ppm). When Keeling first collected his CO_{2} data he travelled around making the measurements at widely spaced locations â€“ but he saw t

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

understand why systems thinking might be useful and know something about how it can be applied in the context of environmental responsibility;

describe the significance of environmental pragmatism and cognitive justice as tools for supporting environmental policy and action.

*Economic Geography*, vol.72, pp. 107â€“30.

*Spaces of Work: Global Capitalism and Geographies of Labour*, London, Sage.

Throughout this unit, a major concern has been to show how the *demand* of the antisweatshop movement that we not only respond to, but take responsibility for, economic injustices, no matter how distant, is an intensely controversial one. Claims by campaigning groups such as Oxfam and Christian Aid that consumer demand for cheap branded goods perpetuates poverty wage levels in the sweatshop industries are countered by claims from the pro-market lobby which point in an altogether differen

The question of who is responsible for factory sweatshops in the poorer regions of the globe remains a passionate political issue, in North America and beyond. Views on how responsibility for overseas sweatshops should be exercised differ between those who believe that it should be left to market forces to improve conditions and those who consider that everyone, as a consumer, bears some responsibility for their perpetuation and should intervene to bring abo

1.4.3 It's all down to connections

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

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: