Question

Without actual division show that each of the following rational numbers is a non-terminating repeating decimal.

(i) `9/35`

Answer 1

`9/35 = 9/(5 ×7)`

We know either 5 or 7 is not a factor of 9, so it is in its simplest form.
Moreover, (5 × 7) ≠ (2^m × 5ⁿ) 
Hence, the given rational is non-terminating repeating decimal.