Question

use dimensional analysis for each problem. how many kilograms are equal to $1.6 \times 10^6$ mg?
options:
0.99 kg
$1.6 \times 10^{-3}$ kg
$1.6 \times 10^{-9}$ kg
1.6 kg

Explanation:

Step1: List unit conversion factors

We know $1\ \text{kg} = 10^3\ \text{g}$ and $1\ \text{g} = 10^3\ \text{mg}$, so $1\ \text{kg} = 10^6\ \text{mg}$, or $\frac{1\ \text{kg}}{10^6\ \text{mg}} = 1$.

Step2: Convert mg to kg

Multiply the given value by the conversion factor.
$$1.6 \times 10^4\ \text{mg} \times \frac{1\ \text{kg}}{10^6\ \text{mg}} = 1.6 \times 10^{4-6}\ \text{kg} = 1.6 \times 10^{-2}\ \text{kg}$$

Answer:

B. $1.6 \times 10^{-2}\ \text{kg}$