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If I take any whole number and divide by 1000 twice then is it only mathematically possible to have a maximum of 6 numbers right of the decimal point.

Example

999 / 1000 / 1000 = 0.000999

58679 / 1000 / 1000 = 0.058679

My maths teacher has set all of the students in our class the task of finding an exception to this rule, I think it cannot be done!

Thanks

mboratko
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cgwebprojects
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    Hint: If you divide a number by $1000$ (any number, not just a whole number), what happens to the decimal point? – mdp Jun 12 '12 at 13:00
  • More hint: dividing by 1000 twice is the same as dividing by...what number? – Gerry Myerson Jun 12 '12 at 13:01
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    How about 123546 / 1000 / 1000 = 0.1234559999999… . Is that cheating? – MJD Jun 12 '12 at 13:01
  • cgwebprojects your teacher joking or cheating;) @Mark, interesting :) – Saeed Jun 12 '12 at 13:06
  • @Mark I've just been trying to find a 1=0.999... question to link to to make that point, and somehow haven't succeeded! – mdp Jun 12 '12 at 13:07
  • @Matt Tried this? – MJD Jun 12 '12 at 13:09
  • @Mark Almost, my search term also included the "1=", which seemed to confuse it. That was the next thing I would have done if I'd been that invested in tracking one down! – mdp Jun 12 '12 at 13:13
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    If the teacher is seriously seeking an answer like $10^6/10^6=0.\overline{9}$, and there is any portion of the grade riding on answering such a question, I would like to kindly suggest more productive exercises. Students shouldn't be subject to the sadism of being forced to find a useless trick like this :P – rschwieb Jun 12 '12 at 13:13
  • @rschwieb I would guess (and hope) that is not the intention. I remember being asked to find examples of impossible things a few times at school in the hope that somebody would work out that and why it was impossible. It's a fairly instructive exercise in a number of ways. – mdp Jun 12 '12 at 13:21
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    @MattPressland Yeah, it can be for the right level of student. I still remember being asked in an introductory algebra course to "invent the Dorroh extension" without having ever seen anything like the Dorroh extension before. That's kind of like telling a student what a commutative domain is and then asking them to figure out how it can be embedded in a field. – rschwieb Jun 12 '12 at 13:42
  • The simplest answer, if your teacher didn't specify that the digits had to be non-zero: $1/10^6 = 0.000001000...$ – Théophile Jun 12 '12 at 16:05

1 Answers1

4

I can see four cases:

  1. He is wrong
  2. He is lying
  3. It's a trick question (like $10^6/1000/1000 = 0.999\ldots$, or base-n numbers)
  4. He wants you to prove that there is no exception.

I hope it's no.4.

Eelvex
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