Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

The simplest fraction for $0.1 63 ¯$ is ____.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The simplest fraction for

0.1 63 ¯

955

.
To express it in the form of

p q

, assume this number as, say x, and write in the expanded form as follows,

x = 0 ⋅ 1636363.......

………... (i)
First shift 1 towards the left of the decimal, by multiplying each side of equation (1) by 10 as follows,

10 x = 1 ⋅ 636363.....

…………. (ii)
To shift the decimal point by two more places to the right, multiply the equation (ii) by 100 on each side as follows,

1000 x = 163 ⋅ 636363.....

…………(iii)
Now subtract equation (ii) from (iii) and simplify as follows,

1000 x − 10 x = 163.636363..... − 1.636363..... 990 x = 162 x = 162990 x = 955

From the above result, we can conclude that,

0.1 63 ¯ = 955

.
So, it is the simplest fractional form of the given repeating decimal.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE