0.14189189189…. can be expressed as a | vedclass

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Question

(d) $0.14189189189....$

$ = 0.14 + 0.00189 + 0.00000189 + .......$

$ = \frac{{14}}{{100}} + 189\left[ {\frac{1}{{{{10}^5}}} + \frac{1}{{{{10}^8}

Vedclass · Accepted Answer

$\frac{{21}}{{148}}$

Vedclass · Answer

(d) $0.14189189189....$

$ = 0.14 + 0.00189 + 0.00000189 + .......$

$ = \frac{{14}}{{100}} + 189\left[ {\frac{1}{{{{10}^5}}} + \frac{1}{{{{10}^8}}} + ....\infty } ight]$

$ = \frac{7}{{50}} + 189\,\left[ {\frac{{1/{{10}^5}}}{{1 - (1/{{10}^3})}}} ight]$$ = \frac{7}{{50}} + 189\,\left[ {\frac{1}{{{{10}^5}}} 	imes \frac{{{{10}^3}}}{{999}}} ight]$

$ = \frac{7}{{50}} + \frac{{189}}{{999 	imes 100}}$

$ = \frac{7}{{50}} + \frac{7}{{3700}} = \frac{7}{{50}} + \frac{7}{{25 	imes 148}}$$ = \frac{{21}}{{148}}$.

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

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