Question

which of the following rational number have non terminating repeating decimal expansion 31/ 3125

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Answer 1

ANSWER:

The Denominator of 31/ 3125 is 3125

Prime Factorisation of 3125 = 5 × 5 × 5 × 5 × 5 = 5^5

As 3125 has no other Prime Factors other than 5,

CONCLUSION:

31/ 3125 is a Terminating Decimal Expansion.

VERIFICATION:

31/ 3125 = 0.00992

RULE -

A Rational Number p/ q is Expressible as a Terminating Decimal only when Prime Factors of q are 2 & 5 only.

✨Happy Learning!✨

Answer 2

It is terminating decimal expansion