(40.00670 x 108.9076) + (500.67805 - 486.078906) 

if we are to follow the rules of significant figures for msthematical operations, the final answer should be written as_________.

The raw calculation gives a result of 4371.6328249200005. However, to apply significant figure rules:

1. **Multiplication (40.00670 × 108.9076)**: The first value (40.00670) has 7 significant figures, and the second value (108.9076) has 7 significant figures. The result should retain 7 significant figures.

2. **Subtraction (500.67805 - 486.078906)**: The result depends on the number of decimal places. Since the first value has 5 decimal places and the second has 6, the result should retain 5 decimal places.

3. **Addition of results**: When adding or subtracting, we look at the least number of decimal places from the addition step, which is 5.

Thus, the final answer should be rounded to 5 decimal places:

\[
4371.63282
\]

This is the correct representation following significant figure rules.

Would you like further clarification or details? Here are some related questions:

1. What are the specific rules for significant figures in multiplication and division?
2. How do significant figures differ when adding and subtracting values?
3. Can you explain the concept of decimal places in significant figure calculations?
4. How do rounding rules apply when combining operations like multiplication and addition?
5. What are some common mistakes when applying significant figure rules?

**Tip**: Always remember, in multiplication and division, the result is determined by the number with the fewest significant figures, whereas in addition and subtraction, it depends on the fewest decimal places.

(40.00670 x 108.9076) + (500.67805 - 486.078906)

Learn how to apply significant figure rules to the problem (40.00670 x 108.9076) + (500.67805 - 486.078906). This covers the rules for handling significant figures in multiplication and addition, with an emphasis on how to round results appropriately. The final answer is presented with 5 decimal places, following significant figure conventions.

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