Answer :

To round the number 553.9637 to the nearest thousandth, you need to follow these steps:

1. Identify the Digit in the Thousandth Place:
- The thousandth place is the third digit to the right of the decimal point. In the number 553.9637, this digit is 3.

2. Look at the Digit in the Ten-Thousandth Place:
- The ten-thousandth place is the fourth digit to the right of the decimal point, which is 7 in this case.

3. Decide Whether to Round Up or Down:
- If the digit in the ten-thousandth place is 5 or greater, you round the digit in the thousandth place up. If the digit is less than 5, you keep the digit in the thousandth place the same.
- Here, the digit in the ten-thousandth place is 7, which is greater than 5.

4. Round the Number:
- Since 7 is greater than 5, you round the 3 (in the thousandth place) up to 4.

Therefore, when you round 553.9637 to the nearest thousandth, the result is 553.964.