To round 6585.364979 to the nearest thousandth, follow these steps:
Identify the thousandth place: In the number 6585.364979, the thousandth place is the third digit after the decimal point, which is 4.
Look at the ten-thousandth place: The digit in the ten-thousandth place (the fourth digit after the decimal point) is 9.
Apply rounding rules: Since the digit in the ten-thousandth place (9) is greater than or equal to 5, you round the thousandth place up by 1.
Final rounded result: The thousandth place (4) becomes 5, so the number rounds to 6585.365
Thus, 6585.364979 rounded to the nearest thousandth is 6585.365