Question

Find the value of

$0.1\bar{8}$

• A. $$\frac{17}{100}$$
• B. $$\frac{27}{90}$$
• C. $$\frac{17}{90}$$
• D. $$\frac{18}{100}$$

Answer 1

Answer:

$$\frac{17}{90}$$

Suppose, x = 0.18̅ 

   

⇒ x = 0.18888.....        ...(i)

Multiply by 10 in equation (i)

10x = 1.8888…..

⇒ 10x = 1 + 0.888..     ...ii)

Multiply by 100 in equation (ii)

100x = 18 + 0.8888     ...iii)

Subtract equation (ii) from equation (iii)

90x = 17

∴ x = 17/90

Short Trick:

⇒ 0.18̅

⇒ (18 – 1)/90

⇒ 17/90