Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Recurring Decimal Number

Question

Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{77}{210}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Let

\frac{77}{210} = \frac{11}{30}

\frac{p}{q}

is terminating if ,

11 and 30 have no common factor,

Therefore, 11 and 30 are co prime.

For denominator = 30 × 2 × 3 × 5

Denominator is not of the form

2 n 5 m

Thus

\frac{11}{30}, \frac{77}{210}

is not terminating repeating decimal.