Q2 of 57 Page 31

Write the decimal expansions of the following rational numbers and decide whether they are terminating or not.

(i)


(ii)


(iii)


(i)



= 0.104


Hence we can see that the denominator is of the form 2m × 5n and hence decimal expansion of 13/125 is of terminating type.


(ii)




= 23.3408


Hence we can see that the denominator is of the form 2m × 5n and hence decimal expansion of 14588/625 is of terminating type.


(iii)




= 0.098


Hence we can see that the denominator is of the form 2m × 5n and hence decimal expansion of 49/500 is of terminating type.


More from this chapter

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3

If p and q are co-prime positive integers then prove that is an irrational number.

 1

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:

(i)


(ii)


(iii)


(iv)


(v)


(vi)


(vii)


3

For the decimal expansions given below decide whether this number is a rational number or not. If it is a rational number then write your note about the prime factorization of its denominator.

(i) 0.120120012000120000….


(ii) 43.123456789


(iii)


1

The sum of the powers of the prime factors of 196 is: