Final answer:
The question involves expressing numbers in scientific notation and determining the appropriate number of significant figures. Operations are conducted based on the provided expressions, ensuring the final answers match the precision dictated by the significant figures.
Step-by-step explanation:
The student's question involves converting numbers into scientific notation and expressing them with the appropriate number of significant figures. Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. Significant figures represent the precision of a number.
For each expression provided, we perform the operation and express the answer in scientific notation:
- a. 217 ÷ 903 = 0.2403, which can be written as 2.403 × 10⁻¹ with four significant figures.
- b. 13.77 + 908.226 + 515 = 1437.006, which can be written as 1.437006 × 10³ to six significant figures.
- c. 255.0 - 99 = 156, which can be written as 1.56 × 10² with three significant figures since 255.0 has four significant figures but the least significant figure dropped out due to subtraction.
- d. 0.00666 × 321 = 2.13786, which can be written as 2.13786 × 10¹ to five significant figures.
In the cases where scientific notation is not explicitly requested, you should still be mindful of significant figures:
- a. 101.2 + 18.702 = 119.902, which is rounded to 119.9 to ensure it has four significant figures as in the least precise value (101.2).
- b. 202.88 - 1.013 = 201.867, which is rounded to 201.87 to maintain the precision as in the least precise value (202.88).