MS4
Index and standard form
Standard form
Standard form is a version of index form. It is used when we need to represent very large numbers,
such as the distances between planets, or very small numbers, such as the sizes of structures inside
cells.
For example, the speed of light is about 300 000 000 metres per second (m/s). It could be easy to
lose track of all those zeros! To help avoid that, and to make it quicker to write, we say that
300 000 000 is the same as 3  10  10  10  10  10  10  10  10 (count the zeros). 300 000 000
is the same as 3 multiplied by 10, eight times over. We can write this as 3  108.
We can do the same for very small numbers. For example, a red blood cell is about
0.000 0065 metres wide. This is the same as 6.5            .
 can be written as 10–1 and so            can be written as 10–6. 0.0000065 in standard
form is 6.5  10–6. (Note: The number part in standard form is always given as a number between 1
and 10.)
You can easily compare numbers in standard form, because the bigger the index number is, the
bigger the number.
1 The circumference of the Earth is about 40 000 kilometres. Write this in standard form.
2 An average human hair is about 0.00015 m wide. Write this in standard form.
3 Write the following as an ordinary numbers.
a 6.4  106
b
4.2  10–3
c
I can…
●
use and interpret units in index form
●
convert numbers into standard form.
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1
8.926  105
d
2.129  10–9