Write whether the decimal expansion is terminating or non terminating (a) (root13)/625 (b)(root 325)/(625×root52)

Question

If it were of form 13/625 It would be terminating as denominator i.e. 625 can be written in the form of(2^n×5^m) (i.e. 2^0×5^4) But here numerator is root 13. Similiarly the second question also poses a problem.

Answer 1

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Answer 2

(a) The quantity √13 is irrational and therefore is non-terminating when expressed as a decimal. Dividing by a rational number does not change the situation.

(b) Here we need to look more closely at whether the two square roots combine: √325/√52=√(325/52)=√(25/4)=5/2. So the square root does rationalise and (b) becomes 5/1250=1/250=0.004, which is terminating.