To round the number 0.07868 to the nearest thousandth, follow these steps:

1. Identify the thousandth place in the number. In 0.07868, the digit in the thousandth place is 8.
2. Look at the digit to the right of the thousandth place, which is the digit in the ten-thousandth place. Here, the digit is 6.
3. If this digit is 5 or greater, round up the digit in the thousandth place by 1. If it is less than 5, leave the digit in the thousandth place as it is.

Since the ten-thousandth digit is 6 (which is greater than 5), you round up the 8 in the thousandth place.

So, 0.07868 rounded to the nearest thousandth is 0.079.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would you round 0.07543 to the nearest thousandth?
2. What is the difference between rounding to the nearest hundredth and thousandth?
3. How do you round 0.12345 to the nearest thousandth?
4. What would be the result of rounding 0.07864 to the nearest thousandth?
5. Why is it important to understand the place value system when rounding numbers?

Tip: When rounding, always pay close attention to the digit immediately to the right of the place value you're rounding to—it determines whether you round up or down.