You want to round 35,678 to the nearest hundreds place. The hundreds place in your number is shown by the red digit here:

35,678

To round 35,678 to the nearest hundreds place...

The digit in the hundreds place in your number is the 6. To begin the rounding, look at the digit one place to the right of the 6, or the 7, which is in the tens place.

Since the 7 is greater than or equal to 5, we'll round our number up by

1. Adding 1 to the 6 in the hundreds place, making it a 7.
2. Changing all digits to the right of this new 7 into zeros.

The result is: 35,700.

So, 35,678 rounded to the hundreds place is 35,700.