The decimal expansion 0.14189189189... can be | vedclass

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Question

(D) Let $x = 0.14189189189...$
This can be written as $x = 0.14 + 0.00189189...$
$x = \frac{14}{100} + \frac{189}{99900}$
$x = \frac{7}{50} + \frac{18

Vedclass · Accepted Answer

$\frac{21}{148}$

Vedclass · Answer

(D) Let $x = 0.14189189189...$
This can be written as $x = 0.14 + 0.00189189...$
$x = \frac{14}{100} + \frac{189}{99900}$
$x = \frac{7}{50} + \frac{189}{99900}$
Simplifying $\frac{189}{99900}$ by dividing the numerator and denominator by $27$, we get $\frac{7}{3700}$.
$x = \frac{7}{50} + \frac{7}{3700} = \frac{7 	imes 74 + 7}{3700} = \frac{518 + 7}{3700} = \frac{525}{3700}$
Dividing both the numerator and denominator by $25$, we get $\frac{21}{148}$.
Thus, the correct option is $D$.

The decimal expansion $0.14189189189...$ can be expressed as a rational number. Which of the following is its equivalent form?

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