If 0-134 - p-q- where p and q are integers and q - 0- then p-q -

Let x=0.134=0.13434 ... nbsp; nbsp; nbsp; ....(i) Multiplying 10 on both sides, we get, nbsp; 10x = 1.343434 ... — (ii) Multiplying 100 on both si ...

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Standard IX

Mathematics

Rational Numbers

If 0.134 = 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 10 on both sides, we get, $10 x = 1.343434 . . .$ ---- (ii)

Multiplying 100 on both sides, 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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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 10 on both sides, we get, 10x=1.343434... ---- (ii) Multiplying 100 on both sides, 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 $\frac{p}{q} =$ ___