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

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

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