what is the sum of 100.0 g and 0.01 g, expressed in scientific notation and written witht he correct number of significant figures
The Correct Answer and Explanation is :
Answer:
The sum of 100.0 g and 0.01 g is 100.01 g.
Expressed in scientific notation with the correct number of significant figures:
[
1.0001 \times 10^2 \text{ g}
]
Explanation:
- Understanding Significant Figures:
- 100.0 g has four significant figures because the trailing zero after the decimal point counts.
- 0.01 g has one significant figure because only the nonzero digits count.
- Addition and Significant Figures:
- When adding numbers, we focus on the decimal places, not the number of significant figures.
- 100.0 has one decimal place.
- 0.01 has two decimal places.
- The result should be rounded to one decimal place, as the number with the least decimal places determines the final precision.
- Summation:
- (100.0 + 0.01 = 100.01)
- The sum has two decimal places, but we must round to one decimal place.
- Rounding 100.01 to one decimal place gives 100.0.
- In scientific notation, 100.0 is written as 1.000 × 10².
- Final Answer:
- The correctly rounded sum in scientific notation is:
[
1.000 \times 10^2 \text{ g}
] - This preserves four significant figures, matching the number with the fewest decimal places in the original numbers.
Image:
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