Question

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

(i)`64/455`

Answer 1

`64/455 = 64 /(5 ×7 ×13)`

We know 5, 7 or 13 is not a factor of 64, so it is in its simplest form.
Moreover, (5 × 7 × 13) ≠ (2^m × 5ⁿ) 
Hence, the given rational is non-terminating repeating decimal.