S1, Ep 5: How to use Sig Figs.

Caroline Christian, Ph.D.

Now that we have covered why significant figures are important, we have to cover how to use significant figures. Have you ever wondered why they list a number as 3.60, why don't they list it as 3.6? It is because of sig figs! Read on to find out more!

  1. First question is which figures are significant?
  • All nonzero numbers are significant, i.e. 1 - 9.
    • All zeros that appear between two nonzero numbers are significant, for example 101.
    • All zeros that appear before or after a decimal place are significant if they follow a nonzero number. (This rule always trips people up!) For example, 0.0876 has only 3 significant figures because the 0's do not follow a nonzero number. While the number 8760.00 has 6 significant figures because the 0's do follow a nonzero number.

  1. Second question is how do we round to a specified number of significant figures? If you need to round 456,987 to 3 significant figures - you need to keep all the decimal places that are there - just change the last ones to 0, and round up in this case, because the 4th significant figure is above 5. It will be 457,000. If you need to round 0.013004 to 3 significant figures - you need to get rid of numbers, because it follows a decimal point. The answer is 0.0130. What if you needed to round each of these numbers to 1 significant figure? 456,987 = 500,000, and 0.013004 = 0.01.

  2. Third question is now that we know which figures are significant how do we use this information? There are two different processes to remember when using significant figures. The first is addition/subtraction, and the second is multiplication/division.

  • For addition and subtraction the number of sig figs in the answer is based on the least amount of decimal places the numbers have in the problem. For example, suppose we are adding 8760.00 + 0.0876. We see that the first number has only 2 places past the decimal point, and the second number has 4 places past the decimal point. We must use the least amount of places past the decimal point which is 2. So even though the calculator will give you the answer of 8760.0876, the answer expressed to the correct amount of sig figs is 8760.09.

  • In multiplication and division the number of sig figs in the answer is based on the least amount of significant figures the numbers have in the problem. For example, suppose we multiply 8760.00 x 0.0876. Then we must consider how many sig figs each number has. As mentioned before, the first number has 6 sig figs, while the second number has 3 sig figs. Therefore the answer must only have 3 significant figures in it, and it is 767.

02/09/2018