Question

express p/q form 0.37bar

Answer 1

let x= 0.3737...........eq(1)
multiply eq (1) by 100
100×x=100×0.3737
100x= 37.3737.........eq(2)
subtract eq 1 from eq2
99x=37
x=37/99

Answer 2

Rationalising

Given number. $0.\overline{37}$

To find. Express $0.\overline{37}$ in the form $\frac{p}{q}$ where both $p$ and $q$ are integers with $q\neq 0$

Solution.

Let $x=0.\overline{37}$

$\Rightarrow x=0.37373737...$

In order to get a whole number $37$ on the right hand side, we multiply $100$ to both sides:

$\quad 100x=37.37373737...$

$\therefore 100x-x=37.373737...-0.373737...$

$\Rightarrow 99x=37$

$\Rightarrow x=\frac{37}{99}$

$\therefore 0.\overline{37}=\frac{37}{99}$

This is in the required form $\frac{p}{q}$ where $p=37$ and $q=99$.

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