0.14189189189... can be expressed as a ration | vedclass

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(D) Let $x = 0.14189189189...$This can be written as $x = 0.14 + 0.00189189189...$$x = \frac{14}{100} + \frac{189}{99900}$$x = \frac{14}{100} + \frac{

Vedclass · Accepted Answer

$\frac{21}{148}$

Vedclass · Answer

(D) Let $x = 0.14189189189...$This can be written as $x = 0.14 + 0.00189189189...$$x = \frac{14}{100} + \frac{189}{99900}$$x = \frac{14}{100} + \frac{189 \div 27}{99900 \div 27} = \frac{14}{100} + \frac{7}{3700}$To add these,find a common denominator,which is $3700$:$x = \frac{14 	imes 37}{3700} + \frac{7}{3700} = \frac{518 + 7}{3700} = \frac{525}{3700}$Dividing both numerator and denominator by $25$:$x = \frac{525 \div 25}{3700 \div 25} = \frac{21}{148}$Thus,the correct option is $(d)$.

$0.14189189189...$ can be expressed as a rational number.

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