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I have a problem where I have to use 3-digit chopping with numbers such as $\pi^2$, $\pi^3$, $e^3$, etc.

If I wanted to 3-digit chop $\pi^2$, do I square the true value of $\pi$ and then chop, or do I chop $\pi$ first to 3.14 then square it?

J. M. ain't a mathematician
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badjr
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    This very much depends on why you want to chop; if you just want to write a short answer, chop as late as possible. If you want to model a computer, you must chop the result of every operation, because the computer would. – Alfonso Fernandez Mar 27 '13 at 02:22

2 Answers2

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If you chop $\pi$ then square then chop, what you are really chopping is $3.14^2$ not $\pi^2$. So you must take $\pi^2$ and then chop it.

Karl Kroningfeld
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    So for a term such as $\pi^3$, I should enter $\pi^3$ into a calculator, and then chop? – badjr Mar 27 '13 at 02:20
  • @deezy Yes, for reference, I suggest you compare the different methods. For instance squaring 3.14 and chopping gives a slightly lower value than squaring $\pi$ and chopping. – Karl Kroningfeld Mar 27 '13 at 02:23
  • Yeah, I tried it both ways and they gave different results, so I didn't know which method to use. – badjr Mar 27 '13 at 02:27
  • @deezy Well, if you are trying to find the first three digits of $\pi^2$, which is more authentic: taking the first three digits directly, or taking the first three digits of some other number that is somewhat close? – Karl Kroningfeld Mar 27 '13 at 02:36
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As a rule of thumb: Always do the chopping / rounding as late as possible.

azimut
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