Some "Advanced" Addition and Subtraction

Here is a slightly trickier example than those on the previous page. We will take it slowly so that you can see how the rule is used.

We wish to calculate

Before we work this out, let me tell you the (possibly surprising) answer:

Why is this so? If we look at the rule for addition and subtraction, we see that we are told to write out the numbers without using scientific notation (i.e. no powers of 10 allowed). When we do this, the problem becomes simply

To get the correct number of significant figures in the answer, we notice that number 400 was originally written as 4 x 10^2. This number is the one with the "least number of decimal places" (to abuse the phrase - see the next paragraph for clarification), so everything to the right of the "hundreds" column should be ignored. When we round off 370 to one significant figure, we get the advertised answer of 4 x 10^2.

To explain why the hundreds column was chosen as the "cutoff" point, it should be explained that rule 4 was not entirely accurate. Where it says to find the number with least number of decimal places, it really means find the number whose significant figures extend the least amount to the right when you write them all down.

Now that last sentence is not very intuitive, so that is why rule 4 is written as it is. Hopefully, however, this example has cleared up what this rule really means.