Question

What is the difference between

$0.\bar{411}$ and$0.\bar{333}$ ?

• A. $$\frac{78}{999}$$
• B. $$\frac{78}{9999}$$
• C. $$\frac{78}{99|}$$
• D. $$\frac{780}{99}$$

Answer 1

Answer:

$$\frac{78}{999}$$

Suppose x = 0.411411411…….∞      ---- (1)

Multiplying equation (1) by 1000, we get

⇒ 1000x = 411 + 0.411411……∞

⇒ 1000x = 411 + x

⇒ 999x = 411

⇒ x = $\frac{411}{999}$

Similarly,

$0.\bar{333}$ = $\frac{333}{999}$

∴ Their difference = $\frac{411}{999}-\frac{333}{999}$

$=\frac{78}{999}$