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5. 80710000= ? 1 35 Answers Give yourself 5 marks for each correct answer. Total scores of 20 and 25 show that you understand the programme. A score of 15 means that you need a further look at some of the frames. A score of 10 and under means that you really need to work through the programme again. The numbers in brackets after the answers are the frame numbers relating to the question. Read these frames first if your answer is wrong. You will most likely realise where your mistakes occurred. However, if you have any doubts, re-read the whole chapter.

Go to 55 and we will have a look at this another way. 54 Indices Here is the same problem set out in three different ways. We know that the three different ways of expressing the problem as shown above amount to the same thing. Here is the problem written out in full: 10 5 100000 10 3 = 1000 or 100000 -;- 1000 = Q. If 10 5 = 100000 1 100000 1 x - - that is, 10 5 x 10- 3 1 1000 what fraction is 10- 3 ? 55 Indices 1 A. 10- 3 is the same a s - 1000 So, where the base has a positive (+ve) index (not preceded by a minus sign) for example 10 3 , we know that this indicates a whole number.

A base of 8 to the power 5 is written 8 5 . a. In the expression 7 3 , which figure is the base and to what power is the index? Indices A. 7 is the base to the power 3. You will find these three terms, index, power and base, very useful to remember. It is easier to describe 10 4 as 'a base of 10 to the power 4', than to talk about 'a whole number 10 and the figure above and to the right of the whole number'. What is more important, it is technically more correct. As an engineer, you would find it very laborious if technical terms were not expressed in some form of shorthand.