Question

Express 3.6 bar on 6 in form of p/q

Answer 1

let x is 3.6 bar
10x is 36.6 bar
10x -x is 36.6 bar minus 3.6 bar
9x is 33
x is 33/9
x is 11/ 3

Answer 2

The expression for $3.\bar6$ in the form of  $\frac{p}{q}$ is $3.\bar6 = \frac{11}{3}$

Let x=3.6 (Pure recurring decimal)

i.e. x = 3.66666......  {i}

Multiplying eq.{i} by 10, we get:

10x = 36.66666....... {ii}

Subtracting {i} from {ii}, we get:

$10x - x = (36.6666\bar6)-(3.666\bar6)\\\Rightarrow 9x = 33\\\Rightarrow x = \frac{33}{9}\\\Rightarrow 3.\bar6 = \frac{11}{3}$

Hence,

The expression for $3.\bar6$ in the form of  $\frac{p}{q}$ is $3.\bar6 = \frac{11}{3}$

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