Please explain significant figures to me

Question

Hi, so I am taking AP Chem but I'm still iffy on sig figs since my teacher didn't teach it very well last year, and my teacher this year is subtracting points off tests if we have incorrect sig figs.

Can someone briefly explain how to determine how many sig figs to use when we do addition, subtraction, multiplication, division, as well as when we use log functions, and scientific notation?

Much appreciated!

Answer 1

For multiplication and division, the answer should have no more sig.figs. than the least number of s.f. in the numbers being operated on. Ex: 2.005 x 3.21 = 6.4361 = 6.44 (3 s.f. based on 3.21)

For addition and subtraction, the answer should have no more places after the decimal than the least number of places in the numbers being operated on. Ex: 2.005 + 3.21 = 5.215 = 5.22 (2 places after decimal based on 3.21)

When using logs, the number of sig. figs. in the number you are taking the log of tells you how many decimal places to use in the answer. Ex: log 16.43 = 1.215638 = 1.2156 (4 places after the decimal since 16.43 has 4 sig.figs.). Note: This answer 1.2156 has 4 sig.figs., not 5, because we only count the mantissa and not the characteristic, so the 1 preceding the decimal is not counted as significant.

Scientific notation is really no different than what is explained above. 1234 has 4 sig.figs. and 1.234x10³ has 4 sig.figs. The rules for multiplication/division, addition/subtraction and logs are still the same.