Question

express in p/q form given below​

Answer 1

➲QUESTION :

• Express in p/q form : $\sf2.44 \bar{3} \bar{1}$

☯ GIVEN :

• $\bf {2.44 \bar 3 \bar 1}$.

☯ TO FIND :

• p/q form of $\bf {2.44 \bar3 \bar1}$.

➲SOLUTION :

Let

• $\tt{x = 2.44 \bar 3 \bar 1\: \: \:eq (1)}$

By Multiplying 100 in eq(1) on both sides :

• $\tt{100x = 244 .\bar 3 \bar 1\: \: \: eq(2)}$

By Multiplying 100 in equation (2) on both sides :

• $\tt{10000x = 244 31.\bar3 \bar 1\: \: \: eq(3)}$

By subtracting equation (2) from equation (3) :

$\implies{ \sf{10000x -100x = 244 31.\bar3 \bar1 - 244 .\bar 3 \bar1 }}$

$\implies{ \sf{9900 x = 24187}}$

$\implies\underline {\pink{\boxed { \bf{ x= {\dfrac{24187}{9900} }}}}}$

$\huge {\green{\therefore}}$ p/q form of $\sf {2.44 \bar3 \bar1}$ = $\bf{\dfrac{24187}{9900}}$