Question

The decimal expansions of some real numbers are given below. In each case, decide whether they are rational or not. If they are rational, write it in the form pq. What can you say about the prime factors of q
 0.140140014000140000… (ii) 0.16¯¯¯¯¯
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Answer 1

Answer:

1 . this number is non terminating non repeating thus it is irrational number

2. this number is non terminating repeating thus it is a rational number

there are two number repeating after decimal therefore the prime factor of q is 99

Answer 2

Answer:

(A) We have, 0.140140014000140000... a non-

terminating and non-repeating decimal

expansion. So it is irrational. It cannot be

written in the form of

p

q

·

(B) We have, 0.16 a non-terminating but

repeating decimal expansion. So it is

rational.

Let x = 0.16

Then, x = 0.1616... ...(i)

100x = 16.1616 ...(ii)

On subtracting (i) from (ii), we get

100x – x = 16.1616 – 0.1616

⇒ 99x = 16 ⇒ x = 16

99

The denominator (q) has factors other than