Q3 of 57 Page 31

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)


(i) Since the given decimal expansion has non-terminating expansion which implies that it is an irrational number.

(ii) We know the general form of a rational number is p/q



Now let us find out the prime factorization of the denominator.




Hence the denominator is in the form of 2m × 5n.


(iii) Since the given decimal expansion has non-terminating expansion which implies that it is an irrational number.


More from this chapter

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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)


2

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

(i)


(ii)


(iii)


1

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

 2

If two numbers are written in the form of m = pq3 and n = p3q2 then find the HCF of m, n when p, q are prime numbers: