This isn't a homework question although it may seem like one. We've never really discussed significant figures and it was just introduced to us when we were learning how to solve word problems regarding gas laws.

Find $V_2$ when $V_1=\pu{400 mL}$ and $T_1=\pu{32^\circ C}$ and $T_2=\pu{-12^\circ C}$.

My computation goes like this:

$$V_2=\frac{T_2V_1}{T_1}=\frac{(\pu{261 K})(\pu{400 mL})}{\pu{305 K}}=\pu{342.295082 mL}$$

As per the given, the least number of significant figures is one (from $\pu{400 mL}$). How do I approximate $\pu{342.295082 mL}$ to one significant figure?

I didn't know how to create a search query about this so I went here. Thanks.

  • $\begingroup$ 400 is three significant figures. 0 is as good a figure as any other. $\endgroup$ – Ivan Neretin Sep 16 '18 at 6:00
  • $\begingroup$ 342 the number with least figures determines result figures in this operation. Usually 400 should be written with a bar above the zeros. If we took 400 with just one figure, the result would be 300. $\endgroup$ – user43021 Sep 16 '18 at 6:00
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    $\begingroup$ @IvanNeretin No it isn't. The zeros might be significant. And to solve this question (i.e. report a sensible answer), you'll have to decide for one or the other. $\endgroup$ – Karl Sep 16 '18 at 12:59
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    $\begingroup$ Technically $400$ has 1 significant figure. $400.$ has 3. Though for this problem I think assuming 3 significant figures in $\pu{400mL}$ is reasonable $\endgroup$ – A.K. Sep 16 '18 at 18:27

Assuming the precision of the given volume, $V_1 = \pu{400 mL}$, is only to 1 significant figure (i.e. only the hundreds place digit of "4" is precise), then your final answer would be rounded to $V_2 = \pu{300 mL}$.*

If we were to say that $V_1$ had 3 significant figures, then the final answer would round to the ones place, resulting in $V_2 = \pu{342 mL}$. However, the value would technically need to be written as "$\pu{400\!. mL}$," including the decimal place to denote the precision going out to the ones place, in order to imply 3 significant figures instead of 1.

In general, zeros (to the left of the decimal place) not surrounded by non-zero values are not denoted as "significant." For further rules and guidelines for identifying what numbers are significant, how many significant figures there are, and how addition/subtraction or multiplication/division impact the final answer's significant figures, check out this web page from Northern Kentucky University (recommended search terms for future information on this subject would be "understanding significant figures" or "significant figures rules").

*If difficulty was also found in the process of where to begin rounding the answer from, the key is finding the "rounding digit," which, if you have only 1 significant figure to work with, will be the furthest numerical value to the left. See this page for further tips.

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