Up to a discussion of significant zeros.

A Small Problem Involving Zeros

Suppose you have to measure a certain distance for a race. Using your metre long stick, you patiently measure the distance and come out with a length of exactly 1000 m. Of course, by now you realise this measurement has four significant figures in it.

Your partner measures the same distance using the odometer on his car, which gives readings in kilometres only. He measures the distance as 1 km, which has only a single significant figure.

In order to compare the two measurements, your partner converts his measurement to metres and comes out with 1000 m. Suddenly, his number looks exactly the same as yours, yet you know that your number had four significant figures, whereas your partner's had only one. So, your result was more precise.

How can we avoid this sort of ambiguity?

The answer lies in using scientific notation to write down the two measurements.


On to Scientific notation
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