Write down the decimal expansions of by writing their denominators in the form, where m, n are non-negative integers.

2

Without actually performing the long division, state whether will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

3

Is 43.123456789 is a rational number of the form or not? If yes, write the factors of q.

4

Express 5005 as product of its prime factors.

5

Prove that the square of any positive integer of the form 5q + 1 is of the same form.