Some Reflections About This Example

This example shows that not every problem requires precise measurements for us to be able to extract useful conclusions.

Our aim was not to calculate the mass, volume or value of the lead precisely to, say, five significant figures.

To do this would require information that is not so easily available, such as the fuel economies and distribution of every make of car on the road today.

Our answer probably has only one significant figure of accuracy. However it is still a realistic, useful and workable answer to our query.

We made use of data that is easily available or estimated and set up a calculation that involved not much more than simple mental arithmetic. Our answer is not precise, but it is nevertheless a valuable one. It is appropriate to the problem.

The ability to make rapid and accurate estimates is one you should cultivate in the study of science. Of course, you may wish to refine the estimate at a later stage, in light of more accurate data. For example, in our lead-in-petrol example, we may stumble across the actual density of lead somewhere; this would dramatically improve our estimate of the volume occupied by one tonne of lead.

In the following exercises, we have set out a similar problem (this time from a real life situation) for you to work through. It contains some very surprising conclusions.