Math, asked by thatherasantosh7907, 5 hours ago

Couert•0•_27 in the form of p/q

Answers

Answered by Yuseong
12

Answer:

27/99

Step-by-step explanation:

As per the provided information in the given question, we've to convert \sf 0.\overline{27} in the form of p/q.

Let us suppose,

\sf { x = 0.\overline{27}}

So, x = 0.2727\dots_(1)

As bar is placed over 2 digits after decimal point. So, let's multiply 100 with the terms in the L.H.S and the R.H.S.

\longmapsto\rm { 100(x) = 100(0.2727\dots)}\\

Multiplying 100 on both sides.

\longmapsto\rm { 100x = 27.2727\dots \quad\bf {(2)} }\\

Now, subtract equation (1) from equation (2).

Performing subtraction :

100x = 27.2727...

–⠀ x = 0.2727...

99x = 27⠀⠀⠀⠀

Now, we have,

\longmapsto\rm { 99x = 27}\\

Transposing 99 from L.H.S to R.H.S.

\longmapsto\bf { x = \dfrac{27}{99} }\\

Therefore, the p/q form of \sf{0.\overline{27}} is 27/99.

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