Question

Express 1.2171717------------ in the form of p/q.

Answer 1

Answer:

1205

-------

990

Step-by-step explanation:

x = 1.217171717----

multiply by 10 both sides:-

10x= 12.171717------- (eq 1)

multiply by 100 both sides:-

1000x = 1217.171717---- (eq 2)

subtract eq 1 from 2

1000x-10x= 1217-12

990x= 1205

x=1205

-------

990

Answer 2

$\textbf{\large{\pink{\underline{\underline{Step by step Explanation.}}}}}$

$\textit{\underline{Suppose that,,}}$

$\mathit{x=1.21717......}$

$\mathit{\implies{100x=100\times 1.21717......}}$

$\textit{(On multiplying both sides by 100 )}$

$\mathit{\implies{100x=121.71717......}}$

$\mathit{\implies{100x=120.5+1.21717......}}$

$\mathit{\implies{100x=120.5+x}}$

$\mathit{\implies{100x-x=120.5}}$

$\mathit{\implies{99x=120.5}}$

$\mathit{\large{\implies{x=\frac{120.5}{99}}}}$

$\mathit{\large{\implies{x=\frac{1205}{990}}}}$

$\mathit{\large{\implies{x=\frac{241}{198}}}}$

So,, the p/q form of 1.21717... is

$\mathit</em></strong><strong><em>{\large</em></strong><strong><em>{\implies{\frac{241}{198}}</em></strong><strong><em>}</em></strong><strong><em>}$

$\textbf{\small{\red{\underline{Hope it helps you}}}}$

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