[kodos]

There's something I don't quite get about significant figures.

What I know is that rules for multiplication and division differ from those for addition and subtraction.

But the advice I keep being told when carrying out calculations is keep insignificant figures in your calculator and round up at the end.

Suppose I have some calculation involving both types of operations:



(It's made up)

QUESTION: If I just solved this in my calculator and then round up at the end, how do I know how many sign. figures should my result have? Or should I solve it step by step with successive roundings according to the rules? (This looks worst).

Any advice?

[Borek]

Any advice?

Don't worry too much about sig figs, round at the end.

In the case you have posted you can easily check how many sig figs each expressions has - you don't have to round them to do so.

1.005 -> 4
60.41/1.500 = 40.273(3) -> 4
0.232*1.02 = 0.23664 -> 3

and obviously it is 40.273(3) which defines accuracy of the nominator.

_1.005
40.27333(3)
_0.23664
-----------
41.51477(3)

so there are 4 sig figs in 41.51477(3)

You can do similar analysis for denominator (obviously 6x8.2 will dominate), then calculate the value without rounding any intermediate results, then round it down using normal rules.

But it is a wasted effort, probably the only moment you will do it this way will be during quizz checking if you know how to use sig figs 

[kodos]

That's exactly what I needed. Thank you so much!