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Something about significant figures really confuses me, for instance:

If we are counting, say, apples and we say there are 30 apples, there are exactly 30, should 30 be a 2 significant figures number or a 1 significant figure.

And If I am in a phyiscs exams and a quantity like 30 kg is given, this number should be a 2sf numbers but in the same time if say it was 31 kg and I rounded it to 1 sf it would still be 30 and I would say it's a 1 sf number so I'm really confused.

Manar
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  • Sometimes if they meant this to be a 2 sf number, they will write $30.$ (that’s $30$ with a decimal point right after it) but I don’t know how common this is. – paulinho Nov 03 '20 at 15:51
  • Still the same confusion arises when the quantity $300$ is concerned. Is it a 1,2 or 3 s.f. number? – player3236 Nov 03 '20 at 15:52
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    Writing $3\cdot 10^1,\text{kg}$ and $3.0\cdot 10^1,\text{kg}$ might make the number of significant digits more obvious. And if it is not obvious, one has to state it somehow, either with some "$\pm$" error bar or textually. -- Also, with the apples example, with exact numbers there is no margin of error in the order of 1 apple or 0.1 apple or 0.0001 apples, so using the concept of sf seems not advisable – Hagen von Eitzen Nov 03 '20 at 15:52
  • https://math.stackexchange.com/q/3337662/9003 – amWhy Nov 03 '20 at 15:54
  • ^^^ Note from the above link, a number is not necessarily inherently 2 or 3 or .... more significant digits. Any number can be expressed in many different significant figure representation. – amWhy Nov 03 '20 at 15:57

1 Answers1

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This is a confusion, that's why scientists prefer the scientific notation, which clearly indicates the number of significant figures. If your number is $3.0\times 10^1$, then it has two significant figures; if it is $3\times 10^1$, then it has one significant figure.

As for your question, I would say that $30$ in the case of $30$ apples has 2 significant figures, because here the $0$ is significantly counted.

If this sounds confusing, consider this, you have a metre scale (marked up to $30\ \mathrm{cm}$), then if you measure a length of $30\ \mathrm{cm}$, then it has two significant figures as you counted the $0$ significantly, you are able to count $31$ or $32$ as well! However, if you say, you have measured $3000\ \mu\mathrm{m}$ ($\textit{i.e.}\ 3\ \mathrm{mm}$) then none of the zeroes is significant because the $3$ here is significantly counted, the zeroes are not! Any other person could have measured the same and could have said $3500$! That's why only $3$ is significant!

Significant errors count all the digits measured accurately as well as one additional digit to count the errors. In the above case, the $3$ is the additional digit itself!

Hope this is clear :)

ultralegend5385
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