A number, $x$ is represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number is $5.3333333333.....$ Find the value of $p - q$

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Solution

The correct option is C
13

We have $x = 5.3333333......$ ... (i)
Therefore, $10 x = 53.33333333....$ ... (ii)

Subtracting equation (i) from (ii), we get,
$9 x = 48$
$\Rightarrow x = \frac{48}{9} = \frac{16}{3}$

$\Rightarrow p = 16$ and $q = 3$
So, $p - q = 16 - 3 = 13$

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A number, x is represented in the simplest pq form. The decimal expansion of this number is 5.3333333333..... Find the value of p−q

The correct option is C 13 We have x=5.3333333...... ... (i) Therefore, 10x=53.33333333.... ... (ii) Subtracting equation (i) from (ii), we get, 9x=48 ⇒x=489=163 ⇒p=16 and q=3 So, p−q=16−3=13

A number, $x$ is represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number is $5.3333333333.....$ Find the value of $p - q$

The correct option is C
13

We have $x = 5.3333333......$ ... (i)
Therefore, $10 x = 53.33333333....$ ... (ii)

Subtracting equation (i) from (ii), we get,
$9 x = 48$
$\Rightarrow x = \frac{48}{9} = \frac{16}{3}$

$\Rightarrow p = 16$ and $q = 3$
So, $p - q = 16 - 3 = 13$