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E2. A Puzzling Fraction Representation

Show that any positive rational number can be written in the form

where a, b, n, and k are non-negative integers and (nines) represents a string of one or more 9s.

2 comments:

prashant said...

I will like to know that while saying that a fraction can be represented in the desired mentioned form, can we take it as there can be a difference in equality(i.e between the fraction and its converted form -according to that particular expression; as tends to zero but not exactly zero)

Peter Ash said...

No, the equality is exact.