An important and exam oriented question from real numbers chapter in which we have given a rational number 32/147 and we are to prove that the given rational number is a non terminating decimal without actual division

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

32/147

=32/3×7²

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