The answer is:
34.63
Work/explanation:
Rounding to the nearest hundredth means rounding to 2 decimal places (DP).
So we have 2 decimal places, and the 3rd one matters too because it will determine the value of the 2nd DP.
The third DP is 8. Since it's greater than 5, then the value of the 2nd DP will be rounded up. I will add 1 to it.
Remember that we round up when the digit that we're rounding to is followed by another digit that is greater than or equal to 5.
So we round :

Therefore, 34.6286 rounded to the nearest hundredth is 34.63.