Question

Convert 0.ModifyingAbove 393 with bar into a fraction. 1. Assign a decimal to a variable: x = 0.ModifyingAbove 393 with bar. 2. It has 3 repeating digits. Multiply by 10 Superscript 3: (1000) x = 0.ModifyingAbove 393 with bar (1000). 1000 x = 393.ModifyingAbove 393 with bar. minus (x = 0.Modifyingabove 393 with bar). 999 x = 393. 1. Solve for x: x = question mark. Solve for the value of x: What is x = 0.ModifyingAbove 393 with bar as a fraction?


x =

ANSWER; x = 131/333

Answer 1

Answer:

$x=\dfrac{131}{333}$

Step-by-step explanation:

Assign the decimal to a variable:

Let  $x=0.\overline{393}$

Multiply both sides by 1000:

$\implies x \cdot 1000=0.\overline{393} \cdot 1000$

$\implies 1000x=393.\overline{393}$

Subtract the first equation from the second to eliminate the part after the decimal:

$\begin{array}{r r c r}& 1000x & = & 393.\overline{393} \\\\- & x & = & 0.\overline{393} \\\\\cline{2-4} \\& 999x & = & 393 \\\end{array}$

Divide both sides by 999:

$\implies \dfrac{999x}{999}=\dfrac{393}{999}$

$\implies x=\dfrac{393}{999}$

Reduce the fraction:

$\implies x=\dfrac{393 \div 3}{999 \div 3}$

$\implies x=\dfrac{131}{333}$