Is 71/43 a rational number?

1 Answer
George C.
Sep 28, 2016

Yes.

Explanation:

A rational number is a number expressible in the form p/q for integers p, q with q != 0.

To get a decimal representation you can long divide 71/43.

During the long division, the running remainder will take one of the values 0, 1, 2, 3,... 42. SInce there are only finitely many possibilities, the remainder must eventually repeat. If the decimal representation is non-terminating then the running remainder will not take the value 0 and the length of the repeating decimal will probably be a factor of 42 since 43 and 10 are co-prime.

I suspected that this one would repeat after 42 decimal places, but it actually repeats after 21.

71/43 = 1.bar(651162790697674418604)

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