Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The $$6389^{th}$$ digit in this sequence is

From 1 to 9, number of digits used = $$9$$

From 10 to 99, number of digits used = $$2*90=180$$

From 100 to 999, number of digits used = $$3\times\ 900=2700$$

So, total number of digits used till now = $$2700+180+9=2889$$

Remaining digits to be used = $$6389-2889=3500$$

But now we will be using 4 digit numbers starting from 1000

So, the number of 4 digit numbers we can write using 3500 digits = $$\dfrac{3500}{4}=875$$

Since we are starting from 1000, $$875^{th}$$ number will be $$1000+875-1=1874$$

or, we can say $$6389^{th}$$digit will be $$4$$