Consider the rational number which in decimal form is .12345345345345...

It begins with two non-repeating digits followed by a block of 3 digits which repeats.

For the generalized repeating decimal
.[a][b][b][b][b]...

Where [a] has n digits and [b] has m digits.

Find a general way to transform it into a rational number of the form p/r.

(In reply to

A little mistake by Chesca Ciprian)

True. My original intention was to write the above expression in conformity with the other comments.

However, a typographical anomaly on my part, in writing *n *instead of *10^n*, dictated otherwise.

Accordingly, I confirm having corrected the foregoing lacuna in my original post.

*Edited on ***September 28, 2007, 7:30 am**