Question about significant figures

[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.

 

[DeeNos]

I understand your confusion about significant figures. It is a concept that is often taught but can be challenging to apply in practice. In regards to your question, the answer depends on the specific context and purpose of your calculations.

If your calculations are for a scientific experiment or study where precise measurements are critical, it is best to use the exact result from the calculator (option c). This will ensure the most accurate and precise final answer. However, if your calculations are for general purposes and the extra decimal places are not necessary, it is acceptable to use the rounded result (option a).

Ultimately, the key is to be consistent in your use of significant figures throughout your calculations. If you choose to use the rounded result, make sure to carry that same number of significant figures throughout your subsequent calculations. If you choose to use the exact result, make sure to use the full number of significant figures in all calculations. This will help maintain accuracy and avoid errors in your final answer.

Additionally, it is important to note that significant figures are a way to represent the precision of a measurement, not its accuracy. Therefore, it is important to also consider the limitations and uncertainties of your measurements when using significant figures in calculations.

Overall, the best approach is to carefully consider the purpose and context of your calculations and use significant figures in a consistent and accurate manner. I hope this explanation helps clarify any confusion about significant figures.