This question is taken from real numbers in which we have given a rational number 77/210 and we have to prove that the given rational number is a nonterminating decimal.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1C, question no 2(v)

77/210

=77/(2×3×5×7)

=11/(2×3×5)

## 2, 3 or 5 is not factor of 11 so given fraction is in its simplest form.

and, (2×3×5)≠(2^m×5^n)

hence given fraction is non -terminating repeating decimal.