UPSC CDS Math Decimal Fraction Questions

Remember:
Let x=

p

q

,where p and q are co-prime integers, q≠0 be a rational number. If the prime factorisation of q is not of the form2m×5n, where m and n are non-negative integers, then x=

p

q

has a decimal expansion, which is non-terminating and repeating.
Consider the rational number

17

16

17

6

=

17

2×3

Since the prime factorisation of6=2×3 is not of the form
2m×5n,So 17/6 has non-terminating and repeating decimal expansion.