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I have a beaker which goes up in $0.5~\mathrm{mL}$ increments and my teacher told me that my measurement $(15.50~\mathrm{mL})$ was incorrect, and instead the answer was $15.5~\mathrm{mL}$. I don't understand. I know that the liquid is between $15.5~\mathrm{mL}$ and $16~\mathrm{mL}$. My estimated digit is $0$ (it looks like it lies on the line), so my answer is $15.50~\mathrm{mL}$. How is it $15.5~\mathrm{mL}$?

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  • $\begingroup$ When you say $15.50$, it assumes that you have the measurement correct up to 2 decimals. Since you're measuring equipment can do only one decimal, you should report it likewise. So, though numerically $15.50 = 15.5$, they mean different in terms of accuracy of reporting. $\endgroup$ – Shailesh Feb 17 '17 at 0:41
  • $\begingroup$ Technically your teacher is correct. Since your beaker only has increments of 0.5 mL, you can only report a volume measurement to the nearest 0.5 mL. However, what you did is also a common practice and appropriate in some cases. Your eyeball can certainly interpolate to within a couple tenths or so by estimating the level of the liquid as you described. You can do this as one element of a calculation for example, but in the end you have to round your final result to the level of accuracy that your beaker measures to, since you don't actually know what the uncertainty of your eyeball is ;) $\endgroup$ – airhuff Feb 17 '17 at 2:49
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    $\begingroup$ @airhuff - That just isn't true. If you have a burette marked to tenths of a ml then as you pointed out you can interpolate to 0.01 ml. The error isn't +/- 0.01 but probably something more like +/- 0.02. But that is a lot better precision and accuracy than rounding off to 0.1 ml. // That being said, teachers make the rules in their classes. $\endgroup$ – MaxW Feb 17 '17 at 3:19
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    $\begingroup$ Now that I've thought about it -- are you sure that your glassware is a beaker? I don't think I've ever seen a beaker graduated that finely. Can you link to a picture of something similar? $\endgroup$ – hBy2Py Feb 17 '17 at 12:04
  • $\begingroup$ If it's actually not a beaker but a graduated cylinder or other volumetric instrument, see also: Using sigfigs when measuring with an instrument with marks other than powers of ten? $\endgroup$ – Loong Feb 17 '17 at 12:16
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It may have to do with the fact that it's a beaker, rather than some other kind of glassware.

First, beakers are poor vessels for volumetric measurements due to their large diameter/height ratios. You have to add a lot of liquid, relatively speaking, in order to increase the height of the fill level by (say) a millimeter, and that means the uncertainty in the fill volume is large.

As well, beakers are usually not graduated precisely. Thus, even if you very very carefully fill the beaker to exactly the $15.5~\mathrm{mL}$ line with liquid, there's a very real chance that the line doesn't actually correspond exactly to a $\mathit{15.5~mL}$ fill volume.

So, unlike with a piece of glassware specifically made for accurate volumetric measurements, such as the burette mentioned by MaxW in a comment, it is likely not appropriate to assign more significant figures to a beaker measurement than are "available" in the graduation increment.

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