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\(\frac{4}{11} = \frac{4}{11} * 100 = 36.36 = 0.36363636\)

=> 36 is a repeated pattern so the 22nd digit after decimal will be 6 and the 23rd digit will be 3.

Answer A
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To quickly convert between fractions and decimals, it is suggested that we memorise some key conversions: (From these, many many others can be derived.)

1/2 = 0.5
1/3 = 0.3333...
1/4 = 0.25
1/5 = 0.2
1/9 = 0.1111....
1/10 = 0.1
1/11 = 0.090909...

Now, let’s derive some more from these:

3/2 = 3(1/2) = 3(0.5) = 1.5
5/2 = 5(1/2) = 5(0.5) = 2.5
2/3 = 2(1/3) = 2(0.333...) = 0.6666...
1/6 = (1/2)*(1/3) = 0.5(0.333...) = 0.1666...
And so on.

Now this question wants 4/11.
This is nothing but 4(1/11) = 4(0.0909....) = 0.363636...

Finally, all odd places after the decimal point have 3s while even places have 6s. Thus, the 23rd digit will be 3, too (since 23 is odd).
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