Question

Express $4.\bar{12}$ in fraction.

• A. $$\frac{4}{33}4$
• B. $$\frac{48}{33}$$
• C. $4\frac{195}{33}$$
• D. $$4\frac{4}{33}$$

Answer 1

Answer:

$$4\frac{4}{33}$$

We can write 4.121212…. = 4 + 0.121212…..

Assume x = 0.121212      ---- (1)

Multiply by 100 in equation (1)

⇒ 100x = 12 + 0.1212…..

⇒ 100x = 12 + x

⇒ 99x = 12

$⇒ x =\frac{12}{99}=\frac{4}{33}$

⇒ 4 + 0.121212....

$⇒ 4 + \frac{4}{33}$ or $4\frac{4}{33}$