Counting Definition of Sig Figs vs. Uncertainty in the Last Digit with Sig Figs

[Eden K 1B]

When using sig figs with concentrations if your numbers were 1.89 and 0.175 and your answer came out to be 0.642 would you leave your answer like that (3 sig figs) or would you round to 0.64 as this takes into account uncertainty in the last digit. To further explain myself, let's say a series of measurements of the length of a branch yield the following results: 1.008, 0.996, 0.999, and 1.001. Although all these measurements may be equally correct, two results (1.008 and 1.001) contain four sig figs according to one definition we learned, while the other results technically have three sig figs. However, all these numbers are written to indicate the uncertainty in the last digit. Thus, should the four results be treated as if they have equivalent sig figs?

[Sam Leistiko 2B]

When using sig figs, you need to specify what operation you are performing. You stated that you are working with "concentrations" - however, the rules for sig figs are different for addition/subtraction and multiplication.

When multiplying, your final answer should have the same number of sig figs as the number with the lowest number of sig figs that was used in the calculation. In your example, because 1.89 and 0.175 both have 3 sig figs, the final answer of 1.89 * 0.175 should also have 3 sig figs.

However, when adding, your sig figs depend on decimal points. Your final answer should have the same number of decimal points as the number used in the calculation that has the least amount of decimal points. So, if you did 1.89 + 0.175, because 1.89 only has two decimal places, you should round to the hundredths place, and your final answer should also have two decimal places.