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

Approximately
`0.042\; {\rm kg \cdot m^(-3)}`.

Step-by-step 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} * \frac{1\; {\rm g}}{10^(3)\; {\rm mg}} * \frac{1\; {\rm kg}}{10^(3)\; {\rm g}} \\ =\; & 10\; {\rm mg} * \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} * \frac{1\; {\rm m^(3)}}{10^(6)\; {\rm mL}} = 2.40* 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 * 10^(-4)\; {\rm m^(3)}} \approx 0.042\; {\rm kg \cdot m^(-3)}\end{aligned}`.