1-666666 - is a rational number and can be expressed in p - q form where p and q are integers- Then the value of p - q isA- The given number has a non-terminating and non-recurring decimal expansion and cannot be represented as p - qB- 7C- 8D- 6

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Writing Decimals as Rational Numbers

1.666666 …… i...

Question

$1.666666......$ is a rational number and can be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers. Then the value of $p + q$ is

The given number has a non-terminating and non-recurring decimal expansion and cannot be represented as $\frac{p}{q}$

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$6$

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$7$

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$8$

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Solution

The correct option is D
$8$

Let $x = 1.6666...$ ... (i)

$10 x = 16.666666...$ ... (ii)
Subtracting equation (i) from (ii), we get,
$9 x = 15$
Hence, $x = \frac{15}{9} = \frac{5}{3}$

$\Rightarrow p = 5$ and $q = 3$
So, $p + q = 5 + 3 = 8$

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1.666666...... is a rational number and can be expressed in pq form where p and q are integers. Then the value of p+q is

The correct option is D 8 Let x=1.6666... ... (i) 10x=16.666666... ... (ii) Subtracting equation (i) from (ii), we get, 9x=15 Hence, x=159=53 ⇒p=5 and q=3 So, p+q=5+3=8

$1.666666......$ is a rational number and can be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers. Then the value of $p + q$ is

The correct option is D
$8$

Let $x = 1.6666...$ ... (i)

$10 x = 16.666666...$ ... (ii)
Subtracting equation (i) from (ii), we get,
$9 x = 15$
Hence, $x = \frac{15}{9} = \frac{5}{3}$

$\Rightarrow p = 5$ and $q = 3$
So, $p + q = 5 + 3 = 8$