How Should Significant Figures Be Handled in Repeated Calculations?

[return42]

I have a question regarding significant figures. I understand the notion well, but am having trouble putting it into practice. My main question is: let's say you divide two numbers of 3 sf each. The result from the calculator is long so you round it to 3 sf. If you need to re-use that result in a later calculation, do you

(a) use the 3 sf rounded figure,
(b) use the number with one additional sf (so 4 sf even though it won't show on paper), or
(c) use the exact same number you got from the calculator (containing up to 10 sf, also won't show on paper) ?

 

[Borek]

c is the most correct approach. b is not bad, although 1 additional digit (called guard digit) is sometimes not enough, 2 or 3 are much better. a is completely wrong.

 

[return42]

Ah OK thanks. Just to make sure, you never actually write the full number used on paper right?

 

[Borek]

No, even when you are reporting some intermediate results you should round them down.

Note that significant figures - although worshiped by some - are just an approximate way of dealing with precision. While listing all possible digits doesn't make sense, relying too heavily on significant figures is about as wrong.