A number -x-was found to be represented in the simplest p-q form- The decimal expansion of this number was found to be 5-3333333333- Find the value of p - q-

Given decimal is nbsp;5.3333333...... Let, x nbsp;= 5.3333333...... nbsp; Therefore, 10x = 53.33333333.... Subtracting x from 10x, we get 10x nbsp;x = ...

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Standard IX

Mathematics

Decimal Expansion of Rational and Irrational Numbers

A number 'x'w...

Question

A number $^{'} x^{'}$ was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.

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Solution

The correct option is D
13

Given decimal is 5.3333333......
Let, $x = 5.3333333......$
Therefore, $10 x = 53.33333333....$
Subtracting $x$ from $10 x$ , we get
$10 x - x = 53.33333.. - 5.33333.. = 48$
$\Rightarrow 9 x = 48$
$\Rightarrow x = \frac{48}{9} = \frac{16}{3} = \frac{p}{q}$
So, $p - q = 16 - 3$
$∴ p - q = 13$

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A number ′x′was found to be represented in the simplest pq form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.

The correct option is D 13 Given decimal is 5.3333333...... Let, x=5.3333333...... Therefore, 10x=53.33333333.... Subtracting x from 10x, we get 10x−x=53.33333..−5.33333..=48 ⇒9x=48 ⇒x=489 =163=pq So, p−q=16−3 ∴ p − q = 13

A number $^{'} x^{'}$ was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.