B Error in approximation to log(223)/log(3) .... senior moment?

AI Thread Summary
The discussion revolves around the approximation of log(223)/log(3) and the confusion regarding the error in the calculations. Initially, an approximation was presented that showed a significant error of 0.0399292, which was later corrected to around 4E-10. The participant noted that the difference between two large numbers should yield a larger error than the difference between smaller numbers, which contributed to their confusion. The error was attributed to selecting the wrong value from the output list during calculations. Ultimately, the participant clarified their misunderstanding and acknowledged the mistake.
Swamp Thing
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This is probably a silly question, but I am really stuck. A possible senior moment, is my only excuse.

Here is an approximation:
##log(223)/log(3) \approx 10818288 / 2198026 ##

So we have:
##log(223)/log(3) - 10818288 / 2198026 = 0.0399292##
which is OK but not great -- the error shows up right at the second decimal.

But when we do this:
##10818288 \times log(223) - 2198026 \times log(3)## it gives us -0.000984652, which looks way better.

I would expect the error between two large numbers to be larger than when the same thing is recast as a difference between two small numbers. Again, it's probably a silly thing that I'm missing, but I haven't been able to find it.
 
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Oops, the 0.0399 is not correct, it is actually around 4E-10. I was printing out 5 or 6 things and picked the wrong value from the output list.
 
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