SIG FIGS

[lauraxie2e]

I was kind of confused on sig figs for answers to questions, for instance if there was a question like (3.8*4.25)/7 would the answer have 2 sig figs or one?

[KDang_1D]

In calculations involving multiplication and division, the least number of sig. figs. is used in the final answer. So in this example, the answer would only have 1 sig. fig. since 7 is only 1 digit.

3.8*4.25 = 16.15 = 16 (2 sig figs. because of 3.8)
16.15/7 = 2.307 = 2 (1 sig fig. because of 7)

[dk0418]

there's an endorsed post in the sig figs section that helps out a lot and describes how other rules as well

[JOtomo1F]

I was confused with sig figs too and found the crash course youtube video to be pretty helpful.

[Nicholas_Gladkov_2J]

With Sig figs there are just two rules:
1) With addition just look at the numbers after the decimal place. Smallest amount of numbers after the decimal is how many numbers are after the decimal there are in the answer
2) With Multiplication, just look at how many numbers there are in totality. Smallest total numbers is amount of numbers in answer.

Just take it step by step if there's addition and multiplication.
Watch out for exact numbers or conversions like 1 m = 1x10^3 mm those just ignore.

[Jiyoon_Hwang_2I]

Also, the zeros may be confusing when considering how many sig figs your answer needs.
Here are two rules that you can use to determine whether a zero is significant:
1. Sandwich Rule: if a zero is "sandwiched" between two significant figures, then the zero is significant. For example, in the number 807, eight and seven are both significant and the zero is between these two numbers so it is also significant.

2. Right-Right Rule: if a zero is to the right of a significant figure AND to the right of decimal, then the zero is significant. For example. in the number 9.000, nine is a significant figure, so the zero in the tenths place is also significant because it is to the right of the nine and to the right of the decimal.

[Milisuryani Santoso 1L]

I was kind of confused on sig figs for answers to questions, for instance if there was a question like (3.8*4.25)/7 would the answer have 2 sig figs or one?

For problems involving only multiplication and division, you just look at the number with the lowest number of sig figs. In this case, that would be 7, meaning you'd only have one sig fig in the answer!

[RyanKopeikin_2I]

For sig figs in answers, you always use the LEAST number of sig figs. For example if you are working with 1305, 1.2, and .033333, you would use 2 sig figs for the answer because 1.2 only has 2 sig figs.

[Tai Metzger 3K]

How necessary is it to use sig figs for all answers? Is it acceptable to round answers to the second or third decimal place?

[Mulin_Li_2J]

Using Sig Figs is pretty necessary because we need to make our calculation as accurate as possible.

Measurements in length, mass, time, etc, often involve certain rounding numbers because we cannot be 100% accurate about those measurements when the smallest unit of our ruler being 1mm, or scale being 1g, or stop watch being 1s. Sig Figs really helps us prevent employing more accuracy than we obtain from measurement. (For example, if your calculation result is 12.300 cm while the smallest unit on your ruler is 1mm, you are using more Sig Figs than you should because simply you cannot in any way be as accurate as 0.001 cm with the current equipment you have.)

Besides, they have specific rules for counting Sig Figs in multiplication/division and addition/subtraction, and those rules are pretty straightforward. Practice more and you'll get it.

[Mulin_Li_2J]

I was kind of confused on sig figs for answers to questions, for instance if there was a question like (3.8*4.25)/7 would the answer have 2 sig figs or one?

I think the answer to this question really depends on the context, which, in this case, is specifically how do you get the number 7. If the number 7 is obtained from a procedure like counting how many cans in a recycle box, then the number 7 is a 100% accurate measurement because you are counting with the smallest unit of cans. And you do not need to take a 100% accurate measurement into account when deciding Sig Figs because it won't make your calculation result to be too accurate. (Remember the whole point of Sig Figs is to prevent more accuracy of the result than it should be) In this case, you just ignore 7, and the final number Sig Figs would be determined by other numbers in the calculation, which are 3.8 and 4.25. So the final number of Sig Figs should be 2.

If, on the other hand, the number 7 is not a 100% measurement, which is probably because the smallest unit of your measurement method is not small enough to get the true value, you need to consider 7 when deciding the final number of Sig Figs. So the answer should be only 1 Sig Fig.

[ayushibanerjee06]

How necessary is it to use sig figs for all answers? Is it acceptable to round answers to the second or third decimal place?

It is necessary to use sig figs for any question. And it depends on the lowest # of sig figs given to you in the question. For example, if the numbers in the question all have 3 sig figs, your final answer should have 3 sig figs as well.