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

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Irrational Numbers

If 0.1 34= p ...

Question

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

$\frac{134}{999}$

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$\frac{134}{990}$

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$\frac{133}{999}$

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$\frac{133}{990}$

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Solution

The correct option is D
$\frac{133}{990}$

Let $x = 0.1 ¯ ¯¯¯¯ ¯ 34 = 0.13434 . . .$ ....(i)

Multiplying by 10 on both sides, we get $10 x = 1.343434 . . .$ ---- (ii)

Multiplying by 1000 on both sides of (i), we get $1000 x = 134.343434....$ ---- (iii)

Subtracting (ii) from (iii), we get

$990 x = 133$

$\Rightarrow x = \frac{133}{990}$

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Question 2
A number of the form $\frac{p}{q}$ is said to be a rational number, if
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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 $\frac{p}{q} =$ ___