Question

The value of \[ \frac{0.004560 \times 1200}{3.00 \times 10^{-2}} \] in correct significant figures is

• A. \(1.8\times10^2\)
• B. \(1.824\times10^2\)
• C. \(182.40\)
• D. \(182\)

Hint:

For multiplication and division, \[ \boxed{ \text{Result should have the same number of significant figures as the quantity with the least significant figures.} } \]

Answer 1

The Correct Option is A

Step 1: Calculate the numerical value. \[ \frac{0.004560 \times 1200}{3.00\times10^{-2}} = \frac{5.472}{0.03} = 182.4 \]

Step 2: Determine significant figures. \[ \begin{aligned} 0.004560 &\rightarrow 4 \text{ significant figures} 1200 &\rightarrow 2 \text{ significant figures} 3.00\times10^{-2} &\rightarrow 3 \text{ significant figures} \end{aligned} \] The final answer must contain the least number of significant figures, i.e., \[ \boxed{2\text{ significant figures}.} \]

Step 3: Round the result. \[ 182.4 \approx 1.8\times10^2 \] Hence, \[ \boxed{(A)} \] is the correct answer.