Question

A 240-mL cup of low‑fat milk contains 10 mg of cholesterol. Express the cholesterol concentration in the milk in kilograms per cubic meter.

Answer 1

Answer:

Approximately $0.042\; {\rm kg \cdot m^{-3}}$.

Explanation:

Note the unit conversion for mass:

$1\; {\rm g} = 10^{3}\; {\rm mg}$.

$1\; {\rm kg} = 10^{3}\; {\rm g}$.

Therefore:

$\begin{aligned}& 10\; {\rm mg} \times \frac{1\; {\rm g}}{10^{3}\; {\rm mg}} \times \frac{1\; {\rm kg}}{10^{3}\; {\rm g}} \\ =\; & 10\; {\rm mg} \times \frac{1\; {\rm kg}}{10^{6}\; {\rm mg}} \\ =\; & 10^{-5}\; {\rm kg}\end{aligned}$.

Similarly, for volume:

$1\; {\rm mL} = 1\; {\rm cm^{3}}$.

$1\; {\rm m^{3}} = 10^{3}\; {\rm dm^{3}} = 10^{6}\; {\rm cm^{3}}$.

Thus, $1\; {\rm m^{3}} = 10^{6}\; {\rm mL}$.

$\begin{aligned}& 240\; {\rm L} \times \frac{1\; {\rm m^{3}}}{10^{6}\; {\rm mL}} = 2.40\times 10^{-4}\; {\rm m^{3}}\end{aligned}$.

Divide mass by volume to find the mass-to-volume ratio:

$\begin{aligned}\frac{10^{-5}\; {\rm kg}}{2.40 \times 10^{-4}\; {\rm m^{3}}} \approx 0.042\; {\rm kg \cdot m^{-3}}\end{aligned}$.