Question

1.27 BAR ON 27 EXPRESS IN P BY Q FORM​

Answer 1

Answer:

Step-by-step explanation:

X is equal to p/q fraction.

x be equal to $\rm{1.}{\rm{\overline{27}}}$

x = $\rm{1.}{\rm{\overline{27}}}$ ___________________(1)

That means it will be 1.27272727..... and so on.

Now , considering it on 10x

10x = $\rm{12.}{\rm{\overline{7}}}$

100x = $\rm{127.}{\overline{27}}$ ________________(2)

Now subtracting (2) from (1),

100x -x = $\rm{127.}{\rm{\overline{27}}} - \rm{1.}{\rm{\overline{27}}}$

99x = 126

x = 126/99

Simplifying the fraction we get

x = 14/11

So, p/q = 14/11

NOTE:

Always take an assumption x to find the p/q form of non terminating numbers.

Answer 2

✯✯ QUESTION ✯✯

Express 1.27 bar on 27 in p by q form...

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Let\:x=1.272727........(1)}$

Multiply both sides by 100..

$\longmapsto\tt{x\times{100}=1.272727\times{100}}$

$\longmapsto\tt{100x=127.2727.......(2)}$

Subtract eq. 1 from 2..

$\longmapsto\tt{100-x=127.2727-1.272727}$

$\longmapsto\tt{99x=126}$

$\longmapsto\tt{x=\cancel\dfrac{126}{99}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\orange{x}\pink{=}\green{\dfrac{14}{11}}}}$