Question

Write 2.025 where 25 has bar in P/q form

Answer 1

$\boxed{\underline{\textsf{Rational Numbers :}}}$

$\textsf{Any number that can be}$
$\textsf{expressed in}\: \frac{p}{q}\:\textsf{form}$
$\textsf{where p and q are both}$
$\textsf{integers with a non-zero q,}$
$\textsf{is called a Rational number.}$

$\boxed{\underline{\textsf{Solution :}}}$

$\textsf{Let us take}\: x = 2.0\bar{25}$

$\to x = 2.0252525...$

$\textsf{Then,}\:1000x = 2025.2525...$

$\textsf{and}\: 10x = 20.2525...$

$\textsf{Now, 1000x - 10x = 2025.25.. - 20.25..}$

$\to 990x = 2005$

$\to x =\frac{2005}{990}$ ,

$\to x =\frac{5*401}{5*198}$

$\to \boxed{\bold{x = \frac{401}{198}}}$

$\textsf{which is in the required}\: \frac{p}{q}\:\textsf{form.}$