Question

answer of .404040 bar in p by q form​

Answer 1

Answer :

$\large{\star\:\:\boxed{\bf{0.\overline{40}\:=\:\dfrac{40}{99} }}\:\:\star}$

Explanation :

Given :–

• $\sf{0.\overline{40}}$ is a Irrational number .

To Find :–

• Fraction form of $\sf{0.\overline{40}}$ .

Solution :–

→ Let $\bf{0.\overline{40}}$ = x  -----(1)

Multiplying both the Sides by 100 :-

→ $\bf{40.\overline{40}}$ = 100x  ------(2)

Subtracting Equation(2) from Equation(1) :-

$\sf{\implies 40.\overline{40}\:-\:0.\overline{40}\:=\:100x\:-x}$

$\sf{\implies 99x\:=\:40}$

$\bf{\implies x\:=\:\dfrac{40}{99} }$

∴ $\bf{0.\overline{40}}$ in form of fraction can be written as $\bf{\dfrac{40}{99} }$.