7.3 Using a calculator for scientific notation

In your future studies, you are likely to be doing many calculations with numbers in scientific notation, so it is important that you know how to input them into your calculator efficiently and how to interpret the results.

First of all, make sure that you can input numbers in scientific notation into your calculator. You could do this using the button you used to input powers in Section 1.2, but it is more straightforward to use the special button provided for entering scientific notation. This might be labelled as EXP, EE, E or EX, but there is considerable variation between calculators. Make sure that you can find the appropriate button on your calculator. Using a button of this sort is equivalent to typing the whole of ‘ prefix multiplication of 10 to the power’. So, on a particular calculator, keying 2.5 EXP 12 enters the whole of 2.5 multiplication 10 super 12 full stop

To enter a number such as five multiplication 10 super negative 16 into your calculator, you may need to use the button labelled something like plus minus (as used in Section 2.1) in order to enter the negative power.

To enter a number such as 10 super nine into your calculator using the scientific notation button, it is helpful to remember that 10 super nine is written as one multiplication 10 super nine in scientific notation, so you will need to key in something like 1 EXP 9.

In addition to being able to enter numbers in scientific notation into your calculator, it is important that you can understand your calculator display when it gives an answer in scientific notation. Enter the number 2.5 multiplication 10 super 12 into your calculator and look at the display. Again there is considerable variation from calculator to calculator, but it is likely that the display will be similar to one of those shown in Figure 7.1. The 12 at the right of the display is the power of ten, but notice that the ten itself is frequently not displayed. If your calculator is one of those which displays 2.5 multiplication 10 super 12 as shown in Figure 7.1e, then you will need to take particular care; this does not mean 2.5 super 12 on this occasion. You should be careful not to copy down a number displayed in this way on your calculator as an answer to a question; this could cause confusion at a later stage. No matter how scientific notation is entered and displayed on your calculator or computer, when writing it on paper you should always use the form exemplified by 2.5 multiplication 10 super 12 full stop

Figure 7.1 Examples of how calculators might display the number 2.5 multiplication 1012.

Question 7.7

To check that you can use your calculator for scientific notation, do the following calculations:

    • a. left parenthesis 4.5 multiplication 10 super four right parenthesis multiplication left parenthesis 4.0 multiplication 10 super 11 right parenthesis
  • left parenthesis 4.5 multiplication 10 super four right parenthesis multiplication left parenthesis 4.0 multiplication 10 super 11 right parenthesis equals 1.8 multiplication 10 super 16

    • b. left parenthesis 6.5 multiplication 10 super negative 27 right parenthesis multiplication left parenthesis 2.0 multiplication 10 super negative 14 right parenthesis
  • left parenthesis 6.5 multiplication 10 super negative 27 right parenthesis multiplication left parenthesis 2.0 multiplication 10 super negative 14 right parenthesis equals 1.3 multiplication 10 super negative 40

    • c. 10 super eight division left parenthesis two multiplication 10 super negative 17 right parenthesis
  • 10 super eight division left parenthesis two multiplication 10 super negative 17 right parenthesis equals five multiplication 10 super 24

    If you obtained the incorrect answer five multiplication 10 super 25 , it is likely that you entered 10 multiplication 10 super eight instead of 10 super eight into your calculator. Remember that 10 super eight can be written as one multiplication 10 super eight full stop

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7.2 Going down: powers of ten for small numbers
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8 More about powers and units