Question

select the correct answer.

what is the fractional form of \\(0.\bar{8}\\)?

\\(\bigcirc\\) \\(\frac{8}{10}\\)

\\(\bigcirc\\) \\(\frac{1}{8}\\)

\\(\bigcirc\\) \\(\frac{8}{9}\\)

\\(\bigcirc\\) \\(\frac{8}{11}\\)

Explanation:

Define the repeating decimal

Let \(x\) represent the repeating decimal value:

$$x = 0.\bar{8} = 0.8888\dots$$

Set up an equation to eliminate the repeating part

Multiply both sides of the equation by \(10\) to shift the decimal point one place to the right:

$$10x = 8.8888\dots$$

Subtract the original equation

Subtract the first equation from the second equation to eliminate the infinite repeating decimal part:

$$10x - x = 8.8888\dots - 0.8888\dots$$

$$9x = 8$$

Solve for x

Divide both sides by \(9\) to find the fractional form:

$$x = \frac{8}{9}$$

Answer:

• (A) \(\frac{8}{10}\)
• (B) \(\frac{1}{8}\)</mcq-correct>
• (C) \(\frac{8}{9}\) (Correct answer)

<mcq-option>(D) \(\frac{8}{11}\)