# Significant figures clarification

#### otownsend

This is not a profound physics question, but I hope someone can help since I just started learning physics.

Given the following calculations below, what would be the proper solutions be (incorporating significant figures)?

10.0 + 2.0(3.3333333) = 10.0 + 6.7 = 16.7

Notice that I rounded 2.0(3.3333333) = 16.6666666 to 16.7.

I am not sure if 16.7 is the right answer. I feel that it is 17 since the least precise measurement in the last arithmetic step has only two significant figures, being 6.7.

#### ChipB

PHF Helper
I would stick with 16.7, given that both 10.0 and 6.7 are accurate to one figure after the decimal point.

#### HallsofIvy

If the problem had said just "2" times (3.3333333) I would agree with ChipB. That is, I would think that "2" was an exact value (like counting 2 things). However it is "2.0" which implies a measured amount measure to the "nearest tenth" (the actual amount could be anywhere from 1.95 to 2.05). That is, the least accurate figure is 2.0 which has "two significant figures". A calculation cannot be more accurate than the least accurate figure in the calculation. So this should be given to two significant figures: 17.

#### otownsend

It seems that there is no universal standard about when the most ideal moments one should round in a calculation. If you agree with that, for now I'll just stick to some of the more general rules about significant figures and then I'll try to use common sense from there. Thanks for your help!