In the last video you learned about the importance of significant figures. When you use too many significant figures, it misrepresents how precise your measurements are. But this becomes even trickier when we get calculations involved. Fortunately, we have rules in place to help us determine the correct number of sig figs to use when we are doing math with our measurements. We have one rule for multiplication and division, and another rule for when we are adding and subtracting.

First, let’s look at the rule for multiplication and division. The rule here is that when you are carrying out multiplication or division, the answer cannot have more significant figures than either of the original numbers. That is to say, look at the numbers you are multiplying or dividing. Whichever one has fewer sig figs, that’s how many sig figs your answer will have.

For example, say we’re finding the area of a rectangle that’s been measured to be 1.2 meters wide by 4.45 meters long. The first measurement has 2 sig figs, and the second measurement has 3. The lower of these is the first measurement, with only 2 sig figs, and that’s how many our answer will have.

So, if you enter this problem into a calculator, you’ll get an area of 5.34 square meters. But this is more than our limit of 2 sig figs, so we have to round off that last decimal, leaving us with 5.3 square meters, and this satisfies the 2 sig fig limit.

Now let’s look at how we deal with addition and subtraction, because it is done a little differently. The rule here is that when you are carrying out addition or subtraction, the answer cannot be more precise – for example, more decimal places – than either of the original numbers.

So before, with multiplication and division, we were looking at the number of significant figures, but with addition and subtraction, we are only concerned with place value.

For example, say we are finding the sum of 6.2 grams and 4.625 grams. Well, 6.2 grams is precise to the tenths place, while 4.625 grams is precise to the thousandths place. The less precise of these numbers is 6.2 grams.

Now, if we enter this into our calculator, we get 10.825 grams, but our answer can only be precise to the tenths place. So we round off those last two digits, and our final answer is 10.8 grams. This satisfies the limit that our answer cannot be more precise than either of the original values. Notice that in this situation, our final answer has 3 sig figs, different than either of our original values.

When we consistently apply these two rules, it allows people within the sciences to accurately convey the precision of their measurements to other scientists.