Question

Convert $0.\bar{6}$ into a fraction:

• A. $$\frac{2}{3}$$
• B. $$\frac{4}{3}$$
• C. $$\frac{6}{3}$$
• D. $$\frac{2}{6}$$

Answer 1

Answer:

$$\frac{2}{3}$$

Any number in the form of $\frac{a}{b}$ is called fraction.

Let, x = 0.6̅  = 0.6666     ---- (1)

Multiplying above equation by 10, we get

10x = 6.6666      ---- (2)

Subtracting equation (1) from equation (2), we get

10x - x = 6.6666 - 0.6666

⇒ 9x = 6

⇒ x = \farc{6}{9}

∴ $x=\frac{2}{3}$