1. The problem is to round the number 0.009876 to 3 decimal places. 2. Identify the digit at the third decimal place: 0.009876 has digits 0 (1st decimal), 0 (2nd decimal), and 9 (3rd decimal). 3. Look at the digit immediately after the third decimal place to decide whether to round up or down. The fourth decimal digit is 8. 4. Since 8 is greater than or equal to 5, we round the third decimal digit (9) up by 1. 5. Rounding 9 up by 1 results in 10, so we carry 1 to the second decimal place. 6. The second decimal place is 0, adding 1 makes it 1, and the third decimal place becomes 0 after carrying. 7. Therefore, the rounded number is 0.010. Final answer: 0.010