I'm doing my online chemistry summer class and significant digits are included, of course. But I'm confused about them because everything I believe is being contradicted. Here's what I mean...

For one assignment we have to add and subtract measurements and "Be sure each answer you enter contains the correct number of significant digits." Well, here are the given questions and answers:

(1) 15.90 mL - 7.770 mL = 8.13 mL

(2) 4.8 mL + 9.927 mL = 14.7 mL

(3) 0.9 mL + 11.870 mL = 12.8 mL

Because of this assignment, I have the impression that to write the final answer in significant digits, it would be by using one of the original numbers with the least amount of numbers after the decimal. What I mean is *when I add the problem from question *(2)*, I get 14.727. But I need to put that answer into the correct significant digits. The two original numbers in the equation for *(2)* are 4.8 and 9.927. I see that for the first number, 4.8, there is only one number left after the decimal place and for the second number, 9.927, there are three numbers after the decimal place. Therefore, I would write my answer, 14.727, with only one number left after the decimal place like 4.8 because it has the least amount of numbers after the decimal place compared to 9.927. My final answer, therefore, would be 14.7. *So, that's my mindset with significant digits and I get the rest of the problems correct.

**But** for a different assignment, my method of finding the significant digits does not work. So the problem they give me is "a chemist measures the volume of the unknown liquid as 0.830 L and the mass of the unknown liquid as 775. g. Calculate the density of the liquid. Be sure your answer has the correct number of significant digits." And we have to put the answer in the format of _____ g / cm^{3}. Anyways, if you solve the problem your answer will be 0.93373... g / cm^{3}. However, we need to put that answer into its correct number of significant digits. Their final answer is 0.934 g / cm^{3}, because they say "There are 3 significant digits in 775. g and 3 significant digits in 830. cm^{3}. Therefore, there are 3 significant digits in the calculated density of the unknown liquid. Be sure to round your final answer correctly."* Basically, they just count how many individual numbers were in the original numbers. Right? Alright. I guess you don't count how many digits are after the decimal place. ***But**, if you look at problem (2)* which says 4.8 mL + 9.927 mL = 14.7 mL, if you count the digits in 4.8 it would be 2 digits, and if you count the digits in 9.927 it would be 4 digits. Then how come the final answer is 14.7 which has 3 digits. Why is the answer not ~15 if we follow the formatting for the second assignment?*

I'm confused.

-Sorry for the large amount of text. I was typing out my mindset so that you could, hopefully, see what is wrong with my mindset.-

Michelle N.

07/20/18