Multiplying versus adding

[samanthaywu]

When adding do you round answer to the number with the least specific decimal places?
Like 12.5 + 9 = 22?
And when multiplying you round to the same number of sig figs as the number with the least number of significant figures?
Like 8.0 * 2.51 = 20 (1 sig fig)

[Charlie Russell 2L]

The given number (in the question) with the LEAST significant figures is the number of significant figures that you use in your answer. This applies to any sort of question.

The second example you gave should have 2 sig figs for this reason.

[Courtney Situ 2B]

Yes!

For significant figures, they follow these rules:

adding/subtracting: round to the nearest place after the decimal point (least decimal places)
(ex. 0.1 + 0.10 + 0.100 = 0.3, you should round to the tenths because of the three added numbers, 0.1 has the closest spot to the decimal point after the decimal point
ex. 0.012 + 0.1100 + 0.01 = 0.13 b/c of the 0.01)

multiplying/dividing: # sig figs should be equal to the smallest # of sig figs of the numbers multiplied/divided
(ex. 1000 * 51.2 = 5120 b/c 1000 has one sig fig
ex. 123 / 123 = 1.00 b/c 123 has three sig fig)

Also, make sure to round only if necessary. I always try to hold off on rounding until the very end of the problem unless the adding/subtracting and multiplying/dividing operations switch. Then, I would have to refer to the correct rule b/c the rules differ depending on your operation.

I did also want to mention that the person above me is correct (there should be two sig figs in example 2). The reason is that 8.0 has two sig figs, not one. Therefore, the answer should be 20. or 2.0 * 10.

Hope this helps!

[Leyna Tran 2D]

I agree! For addition/subtraction, round to the number with the least amount of decimal places. For multiplication/division, round to the number with the least number os sigfigs overall. Also, I would like to add that using a calculator that stores the numbers is really helpful to solve problems in between steps. That way, you can use the whole number and all the decimals from one step to another to keep your answer the most accurate as possible. As said in the previous posts, only round after your final calculation!

[tholz11]

Yup you got it!
As was said above, For addition and subtraction, round to the least amount of decimal places, and when you're multiplying or dividing use the same number of sig figs as the number with the least.

[Dane_Beasley_1E]

Yes, you have it right. When mulitiplying you would use the least number number of Sigfigs and when adding you would use the least number of Sigfigs after the decimal.

[Sidharth Paparaju 3B]

When multiplying/dividing, you keep the lowest amount of sig figs; when adding/subtracting, keep the smallest amount of decimal points.

[Desiree Eshraghi 3A]

Simply, follow the significant figures for the value with the least amount of significant figures (NOT including exact numbers that may be present in certain equations).

[Srikar_Chintala_1E]

Your answer should always be in the lowest sig figs that correspond to a value used in the calculations with the smallest amount of sig figs. For instance, if you add a number with 3 sig figs and another number with 4 sig figs, your answer should have 3 sig figs.

[Anika Scott 3A]

Most people already explained how to round and what you should do, but I just want to emphasize the importance of using zeros as placeholders in order to maintain the correct number of sig figs. There may be incidences where you forget to place the zeros, and then in the end get the incorrect sig figs which could potentially lead to an incorrect answer. So make sure to keep that in mind.

[Nova Akhavan 2F]

Yes! The concept is right however you made a mistake in the multiplication example. 8.0 has 2 significant figures so your answer should have been 20. rather than 20