Question

Without actually performing the long division state whether the following rational numbers will have a

terminating decimal expansion or a non-terminating repeating decimal expansion

(a)

13/
3132 (b) 64/455

Answer 1

(a) 13/3132

      Factorize the denominator we get

       3132   =2×2×3×3×3×29   = 2^2×3^3×29

            There are 2, 3 and 29 also in denominator so denominator is not in form of 2^n*5^m .  Hence  13/3132 is not terminating.

(b) 64/455     

      Factorize the denominator we get

           455     =5 x 7 x 13 

       There are 7 and 13 also in denominator so denominator is not in form of 2^n*5^m .  hence  64/455 is not terminating.

Answer 2

Step-by-step explanation:

(a).13/3132

factorize denominate we her

3132=2×2×3×3×3×29=2^2×3^3×29

therefore.the are 2,3,29 also in decimal so denominator is not in this term of 2^n×5^n.

Hence 13/3132 is not terminating.

(b).64/455

Factor the denominator we het

455=5×7×13.

therefore are 7 and 13 also decimal so denominators is not in this termof 2^n×5^n

Hence 64/455 is not terminating