Question

Express the form of p/q.0.586 (bar on 586)​

Answer 1

Answer:

586/1000 mark me as a brainiest please

Answer 2

Question :-

Express in the Form of $\dfrac{p}{q}$ :- $\mathtt {0.\overline{586}}$

$\begin {gathered} \end {gathered}$

Solution :-

$\begin {aligned} \mathrm {Let\: x} &= 0.\overline{586}\\\\&= \bold {0.586586586...} \ \ \boxed {\text{Eq...(i)}}\end {aligned}$

$\begin {gathered} \end {gathered}$

Since the repeating block 586 has 3 Digits, we Multiply x by 1000 to get -

$\begin {aligned} 1000x &= 0.586586586... \times 1000\\\\ &= \bold {586.586586586...}\ \boxed{\text{Eq...(ii)}} \end {aligned}$

$\begin {gathered} \end {gathered}$

Subtracting $\boxed {\text{Eq...(i)}}$ from $\boxed {\text{Eq...(ii)}}$, we get -

$999x = 586 \Leftrightarrow \bold x = \underline {\boxed {\bf \dfrac{586}{999}}}\ \clubsuit$

$\begin {gathered} \end {gathered}$

Conclusion :-

The $\frac{p}{q}$ form of the given Number $\mathtt {0.\overline{586}}$ is $\bf \dfrac{586}{999}$ .