Question

Taking into account of the significant figures, what is the value of $9.99 \,m - 0.0099 \,m$ ?

• A. 9.9801 m
• B. 9.98 m
• C. 9.980 m
• D. 9.9 m

Answer 1

The Correct Option is B

To solve this problem, we need to determine the value of the expression \(9.99 \,m - 0.0099 \,m\) while considering significant figures.

Step 1: Perform the subtraction

Subtract the values:

\[9.99 \,m - 0.0099 \,m = 9.9801 \,m\]

The raw result of the subtraction is \(9.9801 \,m\).

Step 2: Determine significant figures

Let's consider the number of significant figures in each number in the expression:

• \(9.99 \,m\) has 3 significant figures.
• \(0.0099 \,m\) has 2 significant figures (only the digits '99' count because the zeros are mere placeholders).

For subtraction or addition, we must consider the number of decimal places, not the total number of significant figures. Here:

• \(9.99 \,m\) has 2 decimal places.
• \(0.0099 \,m\) has 4 decimal places.

Thus, the result should have the same number of decimal places as the number with the fewest decimal places, which is 2.

Conclusion: Adjust for significant figures

The result \(9.9801 \,m\) rounded to 2 decimal places gives \(9.98 \,m\). Therefore, considering the significant figures, the final answer is 9.98 m.

Justification for Correct Answer

The correct answer is 9.98 m as it correctly respects the rule of significant figures for subtraction, where the number of decimal places in the result should match the number with the fewest decimal places given.