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

The digit is $4$. The integers through $999$ use $9+90\cdot2+900\cdot3=2889$ digits, leaving $3500=875\cdot4$ digits to reach the target. This ends at the units digit of $1000+874=1874$, whereas adding $875$ to the starting number gives a final digit of $5$.