Question

write the condition satisfied by 210 so that a rational number 77/210 has a non-terminating repeating decimal expansion.

Answer 1

Answer:

Condition satisfied by 210 is that the prime factorization of it is not in form of  $2^n5^m$  , where n , m are non negative integers.

Step-by-step explanation:

We are given number $\frac{77}{210}$ rational no.

Its Decimal Expansion is non terminating repeating.

Prime factorization of 210 = 2 × 3 × 5 × 7

Decimal Expansion of  $\frac{77}{210}$  is Non terminating repeating because Prime factorization of 210 is not of the form $2^n5^m$, where n , m are non negative integers.