Rounding Using Significant Figures

[Caitlin_Murphy_3C]

Hi all! I'm a little confused on when to round using significant figures.
I am finding that rounding varies for each answer in the solutions manual for our textbook. Is there a way to know what to round to in an answer using sig figs?
Thank you!

[Abbey Brandt 1K]

Hi Caitlin!

I used to be very confused about significant figures, so I completely understand where you're coming from! The reason the number of significant figures varies so much in the solutions manual is because every problem gives you a different level of specificity to begin with. If the problem begins with something like "25.92 mg of hydrogen fluoride," (4 significant figures), the decimal point in the answer is less than or equal to the number of decimal places in every term in the. Does that make sense?

[Timothy_Yueh_4L]

When rounding with sig figs, there are generally two rules two follow: one dealing with multiplication and subtraction and the other with multiplication and division. In the first scenario, when you multiply or divide any two values, the final answer in sig figs will equal the least accurate amount of sig figs used to carry out the operation. Ex) 2.45 * 19.32 = 47.334 (original answer) but with sig figs the answer = 47.3 ( 3 sig figs because the least accurate value 2.45 has 3 digits). In the second scenario when you subtract or add, the final answer will equal the least accurate amount of sig figs after the decimal (tenth, hundredth, thousandth,…). Ex) 45.87 – 40.3676 = 5.5024 (original answer) but with sig figs the answer = 5.50 (3 total sig figs however this was determined by the amount of sig figs behind the least accurate amount: hundredth (.87)) . Hope this helped! :)

[MichaelMoreno2G]

Thanks for that explanation Tim. I was also confused on how to round using sig figs but I feel like your explanation actually helped. I'm just curious if we will lose points on tests/exams if we round to the incorrect decimal point.

[Caitlin_Murphy_3C]

Thank you so much! Yes, both those explanations helped a lot.
As for losing points on tests, I think we can receive partial credit if we round to the wrong decimal, but will get 1-2 points deducted if our answer does not have the correct number of sig figs.

[Nawaphan Watanasirisuk 3B]

I think one of the TAs mentioned the maximum point we could lose on sig fig related errors are 4 points. You're supposed to apply the sig fig rules at the very end of calculation, I usually keep a longer sig fig during calculations to avoid any errors.

[Noh_Jasmine_1J]

In multiplying and dividing you always use the smallest number of sig figs between those two numbers and in adding and subtracting you should use the smallest number after the decimal point. For example: 1.23 + 1.5 would be 2 sig figs because there is only one number after the decimal point in 1.5

[nolansheow3G]

I've always kept significant figures running in the calculator, regardless of whether you're using multiplication, division, addition, or subtraction. While the rules above about significant figures is correct, most, if not all tests will allow the use of a calculator, so you can just do all the calculations and round at the very end to the correct number of significant figures.

[Diana Chavez-Carrillo 2L]

What is the rule with the zeros when counting sig figs because I know that there are times you do not count the zero as a sig fig but sometimes you do. When do you know to count the zero as a sig fig?

[Janelle Magaling 3L]

Hi Caitlin!
I heard from my TA that it is best to use all the digits while doing the problem to ensure the most accurate answer and then round the final answer at the end. And you round to the least number of sig figs in the given digits. For example, for 2.55 x 3.5 the answer would be 8.9 and not 8.925 because the given 3.5 has the least sig figs with only 2 sig figs.

[JiangJC Dis2K]

Generally, for multiplication and division problems, you adhere to the least number of significant figures stated in the given numbers for the problem. For addition and subtraction, you go to the least number of decimal places given in the problem.

But for rounding I am also a bit confused. I would guess that you round to the correct number of sig figs after every step along the way. But how many digits out do you go to to round?

For example: if the molar mass is 30.445, does this round to 31 using all three decimal places, or does it remain 30 using only the immediate digit after?