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Is there a method to get the first $n$ digits of a quotient (ex. a thousand digit number divided by a 5 digit number) without dividing all the way through? I suppose long division until $n$ digits are produced will work, but that is not very elegant.

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    $\begingroup$ $12345678901234566777789/54321 \approx 1.2346\cdot 10^{22}/(5.4321\cdot10^4)=2.2727\cdot10^{17}$. If you don't have a calculator, then you could get the first few digits by long division as you say. $\endgroup$ – almagest Apr 18 '16 at 8:56
  • $\begingroup$ @almageat huh I've actually used that idea before and I like it, now I just need to figure out how many digits I need to approximate the dividend by $\endgroup$ – qwr Apr 18 '16 at 17:31

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