Final answer:
To solve the problem 5.08 x 1.2 / 1.90+ 2.0-3.0001 with significant figures, follow the order of operations, keep track of the number of significant figures for multiplication, division, and addition/subtraction, and round the final result to the correct precision.
Step-by-step explanation:
The question asks to solve the arithmetic problem 5.08 x 1.2 / 1.90+ 2.0-3.0001 and express the answer with the correct number of significant figures. In solving this problem, it's important to follow the rules for significant figures while performing mathematical operations. Each step of the calculation must be done with precision, and the final result should be rounded according to the number of significant figures in the least precise measurement used in the calculation.
Step-by-Step Explanation:
First, perform the multiplication and division, following the order of operations (PEMDAS/BODMAS):
- Multiply 5.08 and 1.2.
- Divide the result by 1.90.
- Add 2.0 and subtract 3.0001 from the result.
Next, for each operation, it is critical to consider the number of significant figures:
- The product of 5.08 (3 sig figs) and 1.2 (2 sig figs) should be reported with 2 significant figures because 1.2 has the fewest sig figs.
- When dividing by 1.90 (3 sig figs), the result should maintain 2 significant figures.
- Adding and subtracting should be done based on the least precise decimal place among the numbers involved.
Finally, before rounding off the final answer, it's necessary to consider which digit is to be dropped and whether the subsequent digit requires the answer to be rounded up or down.
In summary, applying significant figures correctly ensures the final reported answer reflects the precision of the measurements involved. The result should be rounded to the right significant figures at the final step to avoid the propagation of errors.