Question About Significant Figures and Rounding

[Jialun Chen 4F]

I remain a little ambiguous when it comes to applying sig figs. Can someone clarify when is it appropriate to round, when do we keep the entire digit, and when are we supposed to use sig figs?

[Alexa Hernandez 3k]

It depends on how you obtained that number. If you used division or multiplication, then the number of significant figures will be determined by the original number with the least amount of significant figures. For Example: 2.5 x 3.42 , 2.5 has the smallest amount of sig. figures with only 2 (you will round of once you get 2 significant figures). Answer: 8.6.

[WesleyWu_1C]

If you use addition or subtraction to obtain your number then you would round in the decimal places but where you round in the decimal places depends on the numbers you used to get your answer. For example, if you were given 3.42 + 2.22513, your final answer would be 5.65 because 3.42 has the least number of decimal places (2 decimal places). So you would round your sum to 2 decimal places which gets you 5.65.

[Ryan Narisma 4G]

Hi! To answer the last part of your question "when are we supposed to use sig figs", I think we use significant figures in any and all of our calculations that we do. Whenever we have to calculate, keep in mind the rules that Alexa Hernandez 3k and WesleyWu_3C mentioned before! I hope this helps.

[Paul Hage 2G]

To add to previous responses, it is also important to keep a few extra decimal places when doing your actual calculations. The final answer should have the correct amount of significant figures determined by the rules mentioned in past replies, but you should not to round to a low amount of significant figures when using your calculator because it could lead to an answer that is off by a very small amount due to the fact that you rounded earlier calculations. When solving a problem involving significant figures, I round to the necessary number of significant figures on paper, but keep the full number stored on my calculator to end up with a more accurate answer if I need to add that value to another number.

[Sean Cheah 1E]

Agree with Paul on all counts. I personally only worry about significant digits at the very end of my calculations and the post below can back me up on that.
https://physics.stackexchange.com/questions/63328/do-you-round-off-insignificant-digits-in-the-middle-of-a-calculation

[VioletKo3F]

Hi, I was also having trouble with sig figs, especially since I was a little rusty from high school chemistry. Like I usually do with everything, I searched it up on Google and I found this site (http://chemistry.bd.psu.edu/jircitano/sigfigs.html) does a good job summing everything up. I also attended a chem workshop today and the ua said that the sig figs are small points, but good points to grab onto on quizzes and tests. I'm pretty sure we'll be using them throughout the year, so I'm sure it doesn't hurt to have them down.

[Diana Chavez-Carrillo 2L]

As a visual learner, I found the following images attached below that have helped me better understand the rules with sig figs. Hopefully, it can help some of you too. In sum, nonzero digits always count as a sig fig. For zero digits, if its inbetween nonzero digits it counts and if the zeros are after the nonzero digit it also counts. However, zeros before nonzero digits do not count (e.g. 0.034 is just 2 sig figs; the zeros before 34 do not count because they are just placeholders). Usually for numbers without a decimal point like 200 is just 1 sig fig but if it were 200. then it would be 3 sig figs. For adding and subtracting, you round your final answer based on the least number of DECIMALS PLACES. When multiplying or dividing, you round your final answer based on the least number of SIGNIFICANT DIGITS. For example, you can look at the two attached images below.

[ThomasNguyen_Dis1H]

I think its all situational. Typically your final answer should be in the correct sig figs. For the steps leading up to the final answer, 3-4 decimal places should be sufficient enough.

[Yejin Ban]

When we add molar masses of elements to get the total matter weight of compounds, should I use the entire number that the periodic table gives? or should I round certain numbers?

[Michelle Shin 4B]

I think for the molar masses given in the periodic table you should round to two places after the decimal, which I believe is generally the rule of thumb.

[Isabella Dal Porto 1H]

Follow-up question...If there is a multiplication/division problem and say 1 mol of _ is being used in the equation, are numbers that are just 1 ignored when considering sig figs? 1 mol only has 1 sig fig but many of the answers to the problems disregard this. Is there a special rule for 1s?

[Sophia Shaka 3L]

For this follow-up question, I don't believe that a question saying 1 mol is used would limit sig figs because it is a exact measurement. Sometimes the question will try to guide you towards the correct number of sig figs, by writing it as 1. mol or 1.00 mol, but I wouldn't think this measurement as 1 mol would limit the answer because it is usually a measurement known with certainty. Not sure if there is some 'special rule' for single digit whole numbers like you ask, but just make sure the number of sig figs in your answer makes sense within the context of the problem.

[Sofia Barker 2C]

In response to the follow-up question, your example illustrates a problem including an exact figure. In this case, it is known that there is exactly 1 mole of __ being used in the equation, which means that the number 1 has an infinite number of sig figs. Usually, problems will indicate that numbers like these are exact, but determining this is entirely situational.

[AGulati_4A]

Watch this video, it is super helpful: https://www.khanacademy.org/math/arithm ... nt-figures


Also, you are simply taking the number with the least amount of sig figs, as you don't want your answer to be more precise than any of the numbers you started with.

[Diana Chavez-Carrillo 2L]

When we add molar masses of elements to get the total matter weight of compounds, should I use the entire number that the periodic table gives? or should I round certain numbers?

I noticed that the periodic table Lavelle has shown us compared to one I had back home has different amount of numbers after the decimal point. So, I did a bit of research because I was curious too if we should round or not. I found that the rule of thumb is to round to 2 digits after the decimal point but I am not sure if Lavelle approves of this or if he wants us to use the exact molar masses on the periodic table.

"Periodic tables will almost always contain a molar mass for each element, but the number of digits after the decimal point that are included vary from table to table. As a rule of thumb, always use the value rounded to two digits after the decimal point."

"Example 2: One periodic table lists the molar mass of Chlorine to be 35.453 grams per mole. Round this to the correct number of digits.
Solution: Use only two digits after the decimal point, making the value that would be used in calculations 35.45."
https://opencurriculum.org/5408/molar-mass/

[505106414]

Is anyone familiar with Dr. Lavelle's rule for rounding to the nearest even number when there are 4 sig figs and you can only have 3?

[William Francis 2E]

Is anyone familiar with Dr. Lavelle's rule for rounding to the nearest even number when there are 4 sig figs and you can only have 3?

I don't think I've heard him talk about this. Is this a rule that isn't standard, but Dr. Lavelle wants us to apply? And what do you mean by the nearest even number if you don't mind elaborating?

[505106414]

Is anyone familiar with Dr. Lavelle's rule for rounding to the nearest even number when there are 4 sig figs and you can only have 3?

I don't think I've heard him talk about this. Is this a rule that isn't standard, but Dr. Lavelle wants us to apply? And what do you mean by the nearest even number if you don't mind elaborating?

A UA at a review session said to round to the nearest even number even if you would round up to an odd number normally (ex: 3.466 would remain 3.46). I had never heard of this before but the UA claimed Lavelle instructs TAs to take off points if you don't do it.

[Alexa Hernandez 3k]

Only round for the final result. If not your final number will be slightly different.
For multiplication and division you go with the number with the least Sig. figures
For adding or subtracting use the number with the least amount of decimal points...

[Micah3J]

Do the significant figures of a constant such as Avogadro's number or Planck's constant matter in our final answer?

[Shail Avasthi 2C]

Don't worry about significant figures until it's time to write your final answer to the problem. While solving the problem, numbers should remain as exact as possible so that your final answer is as accurate as it can be. Then apply significant figure rules to your final answer.

[zfinn]

Do the significant figures of a constant such as Avogadro's number or Planck's constant matter in our final answer?

I'm pretty sure their sig figs don't count since they are constants