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

  • #1
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.
 

Answers and Replies

  • #2
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.
 

Suggested for: Error in approximation to log(223)/log(3) .... senior moment?

Replies
9
Views
677
  • Last Post
2
Replies
44
Views
2K
  • Last Post
Replies
13
Views
873
  • Last Post
Replies
10
Views
806
Replies
6
Views
470
  • Last Post
Replies
1
Views
445
Replies
10
Views
533
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
321
  • Last Post
Replies
4
Views
844
Top