Identify hundredth place: Identify the hundredth place in the number 0.584. The hundredth place is the second digit to the right of the decimal point, which is 8 in this case.
Determine rounding direction: Look at the digit to the right of the hundredth place to determine whether to round up or down. The digit is 4, which is less than 5, so we do not round up the 8 in the hundredth place.
Keep hundredth place digit: Since the digit to the right of the hundredth place is less than 5, we keep the hundredth place digit the same (8) and drop the rest of the digits after the hundredth place.
Final rounded number: The number 0.584 rounded to the nearest hundredth is 0.58.