If 0-1 34- p - q where p and q are integers and q-0- then p - q -A- 134-999B- 134-990C- 100-999D- 133-990

The rational number of the form $\frac{p}{q}, q \neq 0$ , $p$ and $q$ are positive integers, which represents $0.1 ¯ ¯¯¯¯ ¯ 34$ i.e., $(0.1343434......)$ is

Q. Express

3.25

\frac{p}{q}

form where

q \neq 0

and

p, q

are integers

Question 2
A number of the form $\frac{p}{q}$ is said to be a rational number, if
(a) p and q are integers.
(b) p and q are integers and q ≠ 0
(c) p and q are integers and p ≠ 0
(d) p and q are integers and p ≠ 0 also q ≠ 0.

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If 0.1¯¯¯¯¯¯34=pq where p and q are integers and q≠0, then pq= ___

The correct option is D 133990 Let x=0.1¯¯¯¯¯¯34=0.13434... ....(i) Multiplying by 10 on both sides, we get 10x=1.343434... ---- (ii) Multiplying by 1000 on both sides of (i), we get 1000x=134.343434.... ---- (iii) Subtracting (ii) from (iii), we get 990x=133 ⇒x=133990

If $0.1 ¯ ¯¯¯¯ ¯ 34 = \frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$ , then $\frac{p}{q} =$ ___