Question

Express 0.1455555 in p/q form

Answer 1

$\textit{\underline{\large{\underline{\red{Step by step Explanation:-}}}}}$

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

$\mathrm{x=0.45555....}$

$\textit{\underline{Hence,,}}$

$\textit{(On multiplying both sides by 10)}$

$\mathrm{\implies{10x=10\times 0.45555....}}$

$\mathrm{\implies{10x=4.55555....}}$

$\mathrm{\implies{10x=4.1+0.55555....}}$

$\mathrm{\implies{10x=4.1+x}}$

(because x=0.455555....)

$\mathrm{\implies{10x-x=4.1}}$

$\mathrm{\implies{9x=4.1}}$

$\mathrm{\implies{\frac{4.1}{9}}}$

$\mathrm{\implies{\frac{41}{90}}}$

$\textit{\underline{Hence,,}}$

The p/q form of 0.4555..is,,

$\mathrm{\implies{\red{\boxed{\frac{41}{90}}}}}$

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Answer 2

Answer:

131/900

Step-by-step explanation:

First a fall let consider,

x=0.1455555________

now, on multiplying 100 both the side we get,

100x=14.555555_________  ----------------------(1)

Again,

from x=0.1455555___________

On multiplying 1000 both the side we get,

1000x=145.555555__________  ------------------(2)

    Now on doing (2)-(1) we get,

1000x-100x = 145.5555______ - 14.555555_________

900x=131

so,

    x=131/900