Question

The density of a metal is calculated as follows. The weight of \(57.4\) grams is divided by the volume \(6.2\ \text{cm}^3\). Using the approximate rule for significant figures in this calculation, the value of the density, in \(\text{g/cm}^3\), should be reported as:

• A. \(9\)
• B. \(9.3\)
• C. \(9.26\)
• D. \(9.258\)

Hint:

In multiplication or division, the final answer should have the same number of significant figures as the value with the least number of significant figures.

Answer 1

The Correct Option is B

Concept:
Density is defined as mass per unit volume. It tells us how much mass is present in a given volume of a substance. The formula is: \[ \text{Density}=\frac{\text{Mass}}{\text{Volume}} \] In this question, we also need to apply the rule of significant figures. For multiplication and division: \[ \text{Final answer should have the same number of significant figures as the least precise given value.} \]

Step 1: Write the given values.
Mass of the metal is: \[ 57.4\ \text{g} \] Volume of the metal is: \[ 6.2\ \text{cm}^3 \] So, \[ \text{Density}=\frac{57.4}{6.2} \]

Step 2: Calculate the density before rounding.
\[ \text{Density}=9.258064\ldots\ \text{g/cm}^3 \] So the exact calculator value is approximately: \[ 9.258 \]

Step 3: Count the significant figures in the given data.
The value \(57.4\) has three significant figures: \[ 5,\ 7,\ 4 \] The value \(6.2\) has two significant figures: \[ 6,\ 2 \] The least number of significant figures is: \[ 2 \] So the final answer must be reported up to 2 significant figures.

Step 4: Round the calculated value.
The calculated value is: \[ 9.258 \] Rounded to 2 significant figures: \[ 9.258 \approx 9.3 \]

Step 5: Check the options.
Option (A) \(9\) has only 1 significant figure, so it is too rounded.
Option (B) \(9.3\) has 2 significant figures, so it is correct.
Option (C) \(9.26\) has 3 significant figures, so it is not correct according to the rule.
Option (D) \(9.258\) has 4 significant figures, so it is also not correct. Hence, the correct answer is: \[ \boxed{(B)\ 9.3} \]