Question

what is rhe condition fot the decimal expansion of a rational number to terminate ? exlane with help of example​

Answer 1

$\huge \bold{hello}$

➡For the decimal expansion to be terminating, the denominator should be of the form 2^m×5^n.

➡In simple terms, the prime factorisation of the denominator should have 2 or 5 or both in its prime factorisation.

Examples:

↪17/8=Here , the denominator is expressible in the form of 2^m×5^n as the prime factorisation of its denominator is:

8=2×2×2×5^0=2³×5^0

Hence, the decimal expansion of 17/8 is terminating.

↪37/12000

12000=2×2×3×2×2×5×5

12000=2⁴×5²×3¹

Here, the denominator is not in the form 2^m×5^n as it has 3 as one of the factors. Therefore, its decimal expansion will be non terminating repeating.