Question

which option shows the following answer rounded to the correct number of significant figures?
\\(\frac{(3.43 \times 10^3)}{(2.3401 \times 10^6)} = 1.4657493 \times 10^{-2}\\)
\\(\circ\\ 1.4657 \times 10^{-2}\\)
\\(\circ\\ 1.46575 \times 10^{-2}\\)
\\(\circ\\ 1.47 \times 10^{-2}\\)
\\(\circ\\ 1.5 \times 10^{-2}\\)

Explanation:

Step1: Determine significant figures of inputs

The numerator \( 3.43 \times 10^{3} \) has 3 significant figures. The denominator \( 2.3401 \times 10^{5} \) has 5 significant figures. When dividing, the result should have the same number of significant figures as the least precise measurement, so 3 significant figures.

Step2: Round the given value

The given value is \( 1.4657493 \times 10^{-2} \). Rounding to 3 significant figures: look at the fourth digit (5) to round the third digit (6). \( 1.4657493 \approx 1.47 \) when rounded to 3 significant figures.

Answer:

\( 1.47 \times 10^{-2} \) (corresponding to the option "1.47 × 10⁻²")