Question

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

(i) `32/147`

Answer 1

`32/147 = 32/(3 ×7^2)`
We know either 3 or 7 is not a factor of 32, so it is in its simplest form.
Moreover, (3 × 7²) ≠ (2^m × 5ⁿ) 
Hence, the given rational is non-terminating repeating decimal.