### How Many significant figures to use ?

Posted:

**Tue Oct 01, 2019 1:30 pm**How do we determine how many significant figures to add in our final answer?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=9&t=45803

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Posted: **Tue Oct 01, 2019 1:30 pm**

How do we determine how many significant figures to add in our final answer?

Posted: **Tue Oct 01, 2019 1:45 pm**

Usually the significant figures in your answer are based off of the significant figures in the numbers given in the problem. You also usually use the smallest number of sig figs. For example, if the problem gives you 3.40 mol Cl and 17.35 g H, since the lowest number of sig figs is 3 coming from Cl, your answer should have sig figs. You shouldn't be doing too much rounding in terms of your sig figs while you're solving the problem since that can cause precision errors.

Posted: **Tue Oct 01, 2019 1:47 pm**

Also conversion factors don't count toward sig figs so if you have to convert at some point ie 1000 mg per 1 g, don't round your answer to 1 sig fig if that makes sense

Posted: **Tue Oct 01, 2019 8:30 pm**

Usually you can just use the least number of sig. figs. from the information given in the problem since most calculations involve multiplication and division. However, it is important to remember that when adding and subtracting, sig. figs. are determined by the least number of decimal places.

For example: 0.513 + 22.47 = 26.98

For example: 0.513 + 22.47 = 26.98

Posted: **Tue Oct 01, 2019 8:45 pm**

To add on to what the others said, it is true you can generally base your answer off of the smallest number of sig figs in the original numbers. However, you have to be careful not to count definitions like metric conversion factors (as mentioned) or numbers that could have been garnered from counting (e.g if the example says something about 4 beakers of 5.55 g solution each, the final sig fig value is not 1).

Posted: **Wed Oct 02, 2019 10:38 am**

Generally when rounding or using sig figs, looking at the original problem can help you gauge how many sig figs to use, and normally I would look at the LEAST precise measurement (the more decimal places the more precise). For example, if you are given a problem with the values 3.2, 5.72, and 0.32, your answer should have at least 2 significant figures because the least precise measurement rounds to the tenth place. It is important to note, however, that significant figures accounts for NON-ZERO numbers, which means that even though there are three digits in 0.32, it is technically only 2 sig figs. Although, if it were 0.302, it would then be considered 3 sig figs. Hope this helps!

Posted: **Wed Oct 02, 2019 11:44 am**

Keep in mind, significant figures are not only about decimal places. Leading zeros and trailing zeros are still not significant. For example, .0000000078 actually still only has two significant figures. Likewise, 78000000 only has two.

Decimal places do denote significant figures when a number is written in scientific notation. 7.8 * 10^-9 has two significant digits (it is just my first example, but with all the insignificant figures removed). Scientific notation is useful for exactly this reasonâ€”it makes it much easier to quickly visualize exactly how many significant figures you are working with, and ultimately how many significant figures your answer should have.

Decimal places do denote significant figures when a number is written in scientific notation. 7.8 * 10^-9 has two significant digits (it is just my first example, but with all the insignificant figures removed). Scientific notation is useful for exactly this reasonâ€”it makes it much easier to quickly visualize exactly how many significant figures you are working with, and ultimately how many significant figures your answer should have.

Posted: **Wed Oct 02, 2019 11:50 am**

The general rule is to use the least amount of sig figs. Based off the about of sig figs in the values a problem gives you, you make your answer in the least amount of sig figs given. For example: 1.256 + 0.023 = 1.3 , since in the second value, there are only 2 significant figures. You have to be careful with leading zeros and trailing zeros as well, as they have their own rules.

Posted: **Wed Oct 02, 2019 12:04 pm**

Another important piece of info to remember in regards to significant figures is the place of ZEROS in a number. If a number has non-zero figures and zeros all before the decimal point, those are not included in significant figures. For example 12,000,000 only has two significant figures and would be written in scientific notation as 1.2*10^7. Next, if a number has a decimal, then zeros, then non-zero figures, the zeros also will not be counted towards sig figs. For example, 0.00012 only has two significant figures as well and would be written in scientific notation was 1.2*10^-4. Finally, if a number has a decimal, then non-zero figures, then zeros, the zeros WILL BE counted towards sig figs. For example, 0.0001200 has FOUR significant figures and would be written as 1.200*10^-4.

Posted: **Thu Oct 03, 2019 10:42 am**

The general rule is to round your final answer at the end to the same number of significant figures as the number with the least digits. Try not to round your answers before your final answer, though. Otherwise, your answer will not be as accurate as you want it to be.