Question

Couert•0•_27 in the form of p/q

Answer 1

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.