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I am trying to convert $10^{20}$ electron-volt to ton of TNT.

What I know is:

There are $10^{20}$ eVs which is 1 sig fig.

1 electron-volt = $1.602*10^{-19}$ J which is 4 sig figs.

1 ton of TNT = $4.18 * 10^9$ J which is 3 sig figs.

This is my calculation

$10^{20} * (1.602*10^{-19}) = 16.02J$ or $20J$ because of 1 significant digit

$\frac{20}{(4.18 * 10^9)} = 4.78469*10^{-9}$ ton of TNT or $5*10^{-9}$ ton of TNT with 1 significant digit.

I was told this is an incorrect answer. The other answer I tried involved determining the significant figures in the last step so:

$10^{20} * (1.602*10^{-19}) = 16.02J$ $\frac{16.02}{(4.18 * 10^9)} = 3.83254*10^{-9}$ ton of TNT or $4*10^{-9}$ ton of TNT with 1 significant digit.

I've tried $5*10^{-9}$, $4*10^{-9}$, and even $3.83*10^{-9}$ and they are all wrong. I have not been told the correct answer, so I am not sure what I did wrong. Did I make a mistake in my calculation or am I messing up the significant figures?

EmptyStuff
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  • Have you been told the correct answer, or just that yours are wrong? If the former, please edit the question to include it. – Ethan Bolker Jan 31 '18 at 19:39
  • @EthanBolker I have not been told the correct answer, only that the three answers I tried are wrong. – EmptyStuff Jan 31 '18 at 19:41
  • You don't need to drop significant figures in intermediate calculations, usually you round at the end. This is propagation of error – Triatticus Jan 31 '18 at 19:45
  • Google says $3.82929403 × 10^{-9}$ tons of tnt so that much is right. https://www.google.com/search?q=10%5E20+electron+volts+in+tons+of+tnt&ie=utf-8&oe=utf-8&client=firefox-b-1-ab – Ethan Bolker Jan 31 '18 at 19:46
  • @Triatticus Alright thank you. So for this case, since $10^{20}$ is one significant figure, wouldn't that round $3.83 * 10^{-9}$ to $4 * 10^{-9}$ ton of TNT? I tried that but I was told that is incorrect. Is the exponent not -9? – EmptyStuff Jan 31 '18 at 19:47
  • @EthanBolker So wouldn't that make the answer $4 * 10^{-9}$ or is 1 sig fig not the smallest number of significant figures in this calculation? – EmptyStuff Jan 31 '18 at 19:49
  • That's the answer I'd give, so you need more feedback from who or whatever is telling you it's wrong. Perhaps we're both wrong. – Ethan Bolker Jan 31 '18 at 19:49
  • Yeah at this point I would inquire, if this is a webassign or wileyplus type thing it could be wrong – Triatticus Jan 31 '18 at 19:54
  • @EthanBolker I tried $4e^{-9}$ which I know for sure is the correct format for this program (and units aren't needed), and it was marked incorrect. https://i.imgur.com/m3xdRh8.png I'll ask my professor about this. Thanks for the help. – EmptyStuff Jan 31 '18 at 19:57
  • @Triatticus Yeah thank you for the help anyways. I tried $4e^{-9}$ on the online web assignment, and it was marked wrong (https://i.imgur.com/m3xdRh8.png). I'll go ask my professor about this. – EmptyStuff Jan 31 '18 at 19:59
  • I would only round to significant digits at the very end. No way are you getting me to use $3$ instead of $\pi$ in the middle of calculation just because some measurement is inaccurate. Also, on a more philosophical point, how can you really tell that $10^{20}$ isn't three significant digits? – Arthur Jan 31 '18 at 20:15

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