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

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

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

Express 5005 as product of its prime factors.

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