### Instruction: Round $563.5097$ to the nearest hundredth.### Response: To round a number to the nearest hundredth, I need to look at the digit in the thousandths place, which is the third digit after the decimal point.
In this case, the digit is 9, which is 5 or more.
That means I need to round up the digit in the hundredths place, which is the second digit after the decimal point.
The digit in the hundredths place is 0, so rounding it up means adding 1 to it.
That makes the digit in the hundredths place 1, and I need to drop the rest of the digits after it.