We continue our commentary on significant figures – aka significant digits – with how to add and subtract them.  A chemistry or physics tutor deals with this topic periodically.

If you look over my last few posts, you’ll see the accumulation of articles on significant digits.  Today, we cover adding and subtracting, which is a bit trickier than multiplying and dividing.

With adding or subtracting, you need to see the numbers arranged in a column to understand what to do.

Take, for example, 54.28-49.329.

Step 1:  Write the calculation in a column.

Step 2:  Notice the last place on the right where both numbers have a digit.  Draw a cut-off line there.

Step 3:  Realize that any figures to the right of the cutoff are not significant.  This is why, in the case above, the answer is 4.95 in significant figures.

While 54.28 has four significant digits and 49.329 has five, the answer has only three.  Significant figures can be destroyed by subtraction, whereas they can’t be by multiplication or division.  (See the previous post to understand why.)

Here’s another example:  adding this time.

6.26 + 9.1

Here’s our result:

Note that, because the next digit is greater than 5, we round up, giving 15.4.

As we’ve seen, subtraction can destroy significant figures.  Can addition create them?  See for yourself:

Apparently, each addend has only two sigificant digits, while the answer has three.  Some professors may raise their eyebrows at this:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.