Question

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

`77/210`

Answer 1

`77/210 = ( 77 ÷7)/(210 ÷7)`

= `11/30`

= `11/((2 xx 3 xx 5))`

We know 2, 3 or 5 is not a factor of 11, so `11/30` is in its simplest form.
Moreover, (2 × 3 × 7) ≠ (2^m × 5ⁿ) 

Hence, the given rational is non-terminating repeating decimal.