Squares, roots and powers

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# 2.2 Power notation

The notation in Example 6 is called power notation, or index notation. In a number such as 25, the 5 is called the power, or index, of the number.

The squares are particular examples of powers: 92, for example, can be thought of as ‘9 to the power 2’.

For most numbers, calculating powers by hand soon becomes tedious: while you might be quite happy to find 25 or 92, it would take a long and fairly dull time to find 250 or 920 by hand. So you will be using your calculator for most calculations involving powers, even when the numbers themselves are quite simple. However, there is one number whose powers are quite easy to find, namely 10. For example:

one hundred = 10 × 10 = 102 = 100;

one thousand = 10 × 10 × 10 = 103 = 1000;

one million = 10 × 10 × 10 × 10 × 10 × 10 = 106 = 1000 000.

In the same way that 2 can be written as 21 so 10 can be written as 101.

It is also easy to find powers of 1 and 0. 1 × 1 × 1 × … = 1 and 0 × 0 × 0 = 0.

## Example 7

The headings on the place value tables in the OpenLearn course Numbers, units and arithmetic [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] are tens, hundreds, thousands etc. … Write these as powers of ten. What do you think the units columns heading would be as a power of ten?

 ten = 10 = 101 hundred = 100 = 102 thousand = 1000 = 103 ten thousand = 10 000 = 104 hundred thousands = 100 000 = 105 million = 1000 000 = 106

The power of ten increases for each column. So to be consistent, the units column should be 100. Putting 100 into a calculator gives 100 = 1. So the units column is 1 = 100.

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