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

131/333 ………….zzzssssss

Answer 2

`x=(131)/(333)`

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 (999x)/(999)=(393)/(999)`

`\implies x=(393)/(999)`

Reduce the fraction:

`\implies x=(393 / 3)/(999 / 3)`

`\implies x=(131)/(333)`