September 28, 2020, 05:54:06 PM
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### Topic: Significant Figures in Calculations  (Read 127 times)

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#### Meter

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##### Significant Figures in Calculations
« on: September 15, 2020, 10:56:10 AM »
For problems where all the information is given in, let's say, 3 significant figures, should obtained data be rounded to 3 significant figures? For example, if I am doing Gibbs calculations and I am given a value of enthalpy and entropy in 3 sig figs, but my calculator spits out of a result which is in 4 sig figs, do I round that to 3 sig figs and then use that result for the future calculations?

It seems to especially matter when calculating the reaction constant K from $$K = \exp{\left(-\frac{\Delta G^\circ}{RT}\right)}$$ where small differences in rounding of the RHS values can alter the result quite significantly. For example, 4*10100 is a numerically speaking a much bigger number than 3*10100, so it must have some importance (although the same can't be said for large, negative exponents). I understand that it might not make a huge difference in this context, but I'm wondering what is generally considered good practice.

#### Borek

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##### Re: Significant Figures in Calculations
« Reply #1 on: September 15, 2020, 12:24:25 PM »
my calculator spits out of a result which is in 4 sig figs, do I round that to 3 sig figs and then use that result for the future calculations?

No, you do the calculation with as many digits you get, and you round down only the final result.

If you need to copy some of the intermediate numbers manually don't bother with all digits though, just use 2 or 3 guard digits (copy 2-3 digits more than you will report in the end).
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#### Meter

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##### Re: Significant Figures in Calculations
« Reply #2 on: September 15, 2020, 12:58:14 PM »
my calculator spits out of a result which is in 4 sig figs, do I round that to 3 sig figs and then use that result for the future calculations?

No, you do the calculation with as many digits you get, and you round down only the final result.

If you need to copy some of the intermediate numbers manually don't bother with all digits though, just use 2 or 3 guard digits (copy 2-3 digits more than you will report in the end).
Good to know. Thank you!