How does Significant Figures work? [ENDORSED]

[Junxi Feng 3B]

I don't remember how all the sig figs work... Can somebody explain it to me? Like if 1.25 multiply 3.1, how many sig figs should I keep? What about division?

Also, do I have to keep the sig figs for the problems in the homework?

[Robin Cadd 1D]

When you multiply or divide, the number with the fewest significant figures tells you how many significant figures your answer should have. In the example you provided, 1.25 has 3 significant figures and 3.1 has 2 significant figures. 2<3, so your answer should have 2 significant figures. Hope this helps.

[Ruby Tang 2J]

Wanted to add: sig fig rules are different if you're adding or subtracting. With adding or subtracting, your answer would have the same number of decimal places as the least precise measurement. So 4.8-3.96 would be 0.8 (not 0.84 like it would be if following multiplication/division sig fig rules), because 4.8 is precise to the tenths place whereas 3.96 is precise to the hundredths place, so our answer would only be precise to the tenths place.

[KNguyen_1I]

Additionally to note while doing math and sig figs, in the inter-problem calculations try to not round and to keep as exact numbers as possible; only round the last and final answer to the proper number of sig figs (that being the least amount of sig figs present in the data presented, so as the post above has stated).

[Kellylin_4D]

My high school chem teacher used to always stress the importance of significant digits so yes, do keep them in the homework

[WesleyWu_1C]

Besides remembering that for multiplication and division you should use the least number of sig figs and that for addition and subtraction you should use the least number of decimals, you should also learn the specific rounding Professor Lavelle makes note of. If the last digit is above 5, round up and if the last digit is below 5, round down. BUT if the last digit is a 5, you need to be careful. If the last digit is a 5 and there are no more numbers after it, then you would round to the nearest even number. For example, the value is 7.65 and you're rounding to two sig figs. The answer will be 7.60 since there are no numbers after five and the nearest even number is 6. However, if there are numbers after the five in, for example, 4.65123 and you round to two sig figs, then you round up. So in this case the answer will be 4.7.

[sarahsalama2E]

just wanted to add a quick comment--when doing lets say a dilution problem for example, and the given concentration is .0458 M, you should also always present your answer to the same number of sig figs that are used in the question?

[Claire Lo 3C]

In inter-problem calculations, how many sig figs do u keep? Same as the question or one more?

[Daniel Honeychurch1C]

When there are multiple calculations in one problem, don't round until you have your final answer. For the final answer, round to the least number of significant figures of the data given in the problem.

[Robin Cadd 1D]

In inter-problem calculations, how many sig figs do u keep? Same as the question or one more?

As a general rule of thumb, I think you’d keep the same amount of sig figs as the question.

[Chem_Mod]

Dr. Lavelle's website has a great resource on sig figs that covers most of the great responses on this post: https://lavelle.chem.ucla.edu/wp-content/supporting-files/Chem14A/EVERYTHING_YOU_WANTED_TO_KNOW_ABOUT_SF.pdf

[Julia Mazzucato 4D]

Also, calculate significant figures using the values given to you in the problem. Scientific constants would not be used to determine the significant figures of your final answer. So you wouldn't use the SF in Avogadro's number or Planck's constant to calculate the SF in your answer. Always stick to the numbers provided in the original problem, and leave rounding till the end.

[Amy Pham 1D]

Related and important:

Some numbers are exact, meaning they have infinity significant figures.
a) counted objects (ex: 3 dogs is exactly 3 dogs)
b) often, ratios (ex: H:O is exactly 2:1 in water)
c) denominator in averaging (counted number)