Question

Taking into consideration of significant figures, in the conversion relation \(2.0\ \text{m s}^{-2} = X\ \text{km h}^{-2}\), the value of \(X\) is

• A. $2.6 \times 10^4$
• B. $2.592 \times 10^4$
• C. $2 \times 10^4$
• D. $2.592 \times 10^5$
• E. $2.60 \times 10^5$

Hint:

Always match significant figures: - Final answer should have same number of significant figures as given data

Answer 1

The Correct Option is A

Concept: Unit conversion: \[ 1\ \text{m} = 10^{-3}\ \text{km}, \quad 1\ \text{s} = \frac{1}{3600}\ \text{h} \] Also, significant figures must be preserved in the final answer.

Step 1: Convert $\text{m s}^{-2}$ to $\text{km h}^{-2}$.
\[ 1\ \text{m s}^{-2} = 10^{-3}\ \text{km} \times (3600)^2\ \text{h}^{-2} \] \[ = 10^{-3} \times 12960000 = 1.296 \times 10^4\ \text{km h}^{-2} \]

Step 2: Multiply by given value $2.0$.
\[ 2.0 \times 1.296 \times 10^4 = 2.592 \times 10^4 \]

Step 3: Apply significant figures.
Given $2.0$ has 2 significant figures: \[ 2.592 \times 10^4 \approx 2.6 \times 10^4 \]