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1.5 Arithmetic with real numbers

We can do arithmetic with recurring decimals by first converting the decimals to fractions. However, it is not obvious how to do arithmetic with non-recurring decimals. For example, assuming that we can represent and Author(s): The Open University

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1.4 Real numbers and their properties

Together, the rational numbers (recurring decimals) and irrational numbers (non-recurring decimals) form the set of real numbers, denoted by .

As with rational numbers, we can determine which of two real numbers is greater by comparing their decimals and noticing the first pair of corresponding digits
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1.3 Irrational numbers

There is no rational number which satisfies the equation x2 = 2. A number which is not rational is called irrational. There are many other mathematical quantities which cannot be described exactly by rational numbers; for example, where m and n are natural numbers and
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8.1 Benefits of using a calculator

A calculator can help you learn mathematics – it is not a substitute for learning. In fact it can help you see the underlying mathematics in many ways, as in the previous section. Here are some other examples of how it can help you to learn mathematics:

  • Instead of getting engrossed in performing long, sometimes tedious calculations, you can focus your attention on the problem you are trying to solve.

  • You can work with more realistic
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7.6 Consolidation

You have probably learnt quite a lot about your calculator by now. So this may be a good time to pause and consolidate that knowledge. Speaking mathematics aloud and explaining concepts to somebody else are good ways to do this.

Exercise 15: Speakeasy

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7.5 The pi key

The value of the mathematical constant , pronounced pi, is stored on scientific and graphics calculators. The TI-84 has as the second function on
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7.4 Reciprocals

There is a key on most scientific and graphics calculators which will give the reciprocal of a number. This is one over the number. So the reciprocal of 2 is or 0.5. The reciprocal of 4 is Author(s): The Open University

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7.3 Square rooting a negative number

Another problem surfaces if you start with a negative number and try to find its square root. For example try to find the square root of 4 on your calculator. Depending upon how your calculator is set up, you may either get an error message or an unfamiliar number like 2i or 2j. This is because there is no real number which squared will give you the negative number 4. Every real number, whether positive or negative, has a positive square. There are some numbers, ca
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7.2 Square roots

Earlier you met the square function and on most calculators the square root is the second function on the same key. Look to see if this is the case for your calculator and check the calculator handbook on how to use this function. In many cases you will need to press the square root key before the number, instead of afterwards, as for the square key. This is the case on the TI-84. Check that you can find the square root of 25 and of 0.49 (you should get 5 and .7 respectively).

Now find
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The history of the calculator

Ever since recorded mathematics began, people have been making use of mathematical aids. Four thousand years ago, Babylonian scribes were consulting mathematical tables which included multiplication tables, tables of squares and square roots, and tables of reciprocals of numbers. These values were recorded as marks on clay tablets that were then baked hard in the sun—and some have survived to the present day. (There are several originals to be seen in the British Museum.)

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Why study mathematics?

Figure 1.2
Having set out on her mathematical journey, Dawn suddenly remembered that she had forgotten to pack any sandwiches

There are many re
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Introduction

This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognize mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the Calculator Book, Tapping into Mathematics With the TI-83 Graphics Calculator. The unit ends by asking you to reflect on the process of studying mathematics.

In order to complete this unit you will need
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6 Solutions to the exercises

Section 6 contains solutions to the exercises that appear throughout sections 1-5.

Click 'View document' below to open the solutions (15 pages, 468KB).

2 Representing symmetries

In Section 2 we develop an algebraic notation for recording symmetries, and demonstrate how to use the notation to calculate composites of symmetries and the inverse of a symmetry.

Click 'View document' below to open Section 2 (9 pages, 504KB).

Acknowledgements

Unit image

Alist  [Details correct as of 27th June 2008]

 

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


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2 Functions

In Section 2 we give the general definition of a function, and illustrate how functions can be used to describe a variety of mathematical concepts, such as transformations of the plane. We discuss the idea of composing two functions, and the idea of forming the inverse of a function.

Click 'View document' below to open Section 2 (16 pages, 366KB).

Acknowledgements

All written material contained within this unit originated at the Open University

1. Join the 200,000 students currently studying withThe Open University.


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Acknowledgements

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

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

1. Join the 200,000 students currently studyi
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3.2.1 Try some yourself

1 Use the method outlined in Example 9 to estimate each of the following, and then use yo
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2.6 Negative powers

Now look at what happens when the power is negative. What does 10−3 mean? What is the result of the following calculation?

100 ÷ 100 000

What you are actually being asked to find is:

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