The number $$0.124\overline{64}$$​ in the form $$\frac{p}{q}$$​ is equal to:

Correct option is C

Given:

The repeating decimal number:

x =$$0.124\overline{64}$$​

Solution:

Let

x =$$0.124\overline{64}$$​

Multiply by $$10^3 = 1000$$ to shift the decimal point to the right:

1000x = $$124.\overline{64}$$​

Multiply by $$10^2 = 100$$​ again to shift the repeating block completely:

100000x = $$12464.\overline{64}$$​

Subtract the two equations:

​$$(100000x - 1000x) = (12464.\overline{64} - 124.\overline{64})$$​

99000x = 12340

x =$$\frac{12340}{99000}$$​

x $$= \frac{617}{4950}$$​