Another Calculation Example

In this example, we will assume that we have measured the following quantities:

We wish to multiply the first three numbers together and divide that by the product of the last three numbers.

We compute:

The answer we have at this stage is obviously far too accurate for the data we started out with. We now have to consider how precise this answer really is.

Question: What is the least precise measurement in the above list?

Answer: 0.00013 (you didn't get confused by the zeros did you?)

Our answer is only as accurate as the least precise measurement in the calculation. In other words, our answer is accurate to only 2 significant figures and should be written as

Two points to notice about this answer:

1. Firstly, when we round off, we round 205 up to 210. If the first digit after the significant digits is 5 or larger, we round up; otherwise, round down.

2. The second point is that we have written the answer in scientific notation. If we had just written it as 210, the same confusion that we have seen before (in the race measurement example) would have occurred. Was the final zero significant or not? The scientific notation eliminates this problem.

We can state the principle we have uncovered very clearly as: