Is significant figure important for atomic radius calculations?

Calculate the radius of a vanadium atom, given that V has BCC crystal structure, a density of $\pu{5.96 g/cm^3}$, and an atomic weight of $\pu{50.9g/mol}$.

What if we solve this question with $3$ significant figures and $5$ significant figures? What will be different?


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    $\begingroup$ The use of significant figures is a poor man's way of doing error prorogation. With a modern calculator I'd use two extra figures in intermediate calculations (so 5 significant figures since the data has 3), then round final answer to 3 significant figures. The problem is rounding errors that creep into the intermediate calculations. Such rounding errors are the bane of calculations. It is particularly nasty if you're calculating small differences between two big numbers (e.g. 100.45 - 100.23). $\endgroup$ – MaxW Dec 18 '17 at 14:33
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    $\begingroup$ When I first started chemistry I used a slide rule, so three significant figures were all that was possible. The alternative was a single page of logarithms which was good to three significant figures too. Could use a multi-page table of logarithms which was good to four significant figures. Interpolation with log tables would let you do a bit better. $\endgroup$ – MaxW Dec 18 '17 at 14:38
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    $\begingroup$ Different would be the implied error. You have values with 3 significant figures given, if you report 5 significant figures, then you are reporting over-confidently. (Given that you have to use the hard sphere model in your question, the implied deviation that would be caused by only using 2 significant figures would still be minuscule.) $\endgroup$ – Martin - マーチン Dec 18 '17 at 14:45
  • $\begingroup$ So what would you recommend me to do? I'm going to give the density, atomic weight and Avogadro's constant. Should I specify the significant figure as well? $\endgroup$ – Fiv Dec 18 '17 at 14:58
  • $\begingroup$ How should we know? Perhaps for your use the error estimate is not relevant. I'll doubt it, however. $\endgroup$ – Karl Dec 18 '17 at 20:14