Let's calculate each of these expressions step by step.

First expression:

$8.10 + 84.2 - 34.2143$

Step 1: Add 8.10 and 84.2: $8.10 + 84.2 = 92.3$

Step 2: Subtract 34.2143 from 92.3: $92.3 - 34.2143 = 58.0857$

Rounded to 2 decimal places: $58.09$

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Second expression:

$0.042 \times 6252 \div 581$

Step 1: Multiply 0.042 and 6252: $0.042 \times 6252 = 262.584$

Step 2: Divide 262.584 by 581: $262.584 \div 581 = 0.451$

Rounded to 3 decimal places: $0.451$

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Final answers:

1. $8.10 + 84.2 - 34.2143 = 58.09$
2. $0.042 \times 6252 \div 581 = 0.451$

Would you like more details or have any further questions on this?

Here are some related questions to expand your learning:

1. How do you round numbers to a certain decimal place?
2. How does the order of operations affect multi-step calculations like these?
3. How can you check the reasonableness of your answers in calculations like these?
4. What is the significance of significant figures in rounding results?
5. How do you handle rounding when working with scientific notation?

Tip: Always check the number of decimal places or significant figures required for your final answer based on the precision of the given data.