Question

a metal has a density of 8.35 g/ml. a student calculated the volume of a 3.85 kg sample of that metal to be ml. what is the error in this dimensional analysis problem?
3.85 kg × (\frac{1 \text{kg}}{1000 \text{g}}) × (\frac{1 \text{ml}}{8.35 \text{g}}) = ml

(\bigcirc) 1 kg does not equal 1,000 g
(\bigcirc) the kg to g conversion factor is upside down
(\bigcirc) the ml to g conversion factor is upside down
(\bigcirc) 1 ml of the metal does not equal 8.35 g

Explanation:

To convert kg to g, the correct conversion factor is $\frac{1000\ \text{g}}{1\ \text{kg}}$ (since $1\ \text{kg} = 1000\ \text{g}$). In the student's calculation, they used $\frac{1\ \text{kg}}{1000\ \text{g}}$, which is upside down. The other options are incorrect: $1\ \text{kg} = 1000\ \text{g}$ (so first option is wrong), the mL - g conversion factor (density) is used correctly as $\frac{1\ \text{mL}}{8.35\ \text{g}}$ (since density is $8.35\ \text{g/mL}$, so $1\ \text{mL}$ has $8.35\ \text{g}$? Wait, no, density $d=\frac{m}{V}$, so $V = \frac{m}{d}$, so the conversion from g to mL should be $\frac{1\ \text{mL}}{8.35\ \text{g}}$, which is correct. And $1\ \text{mL}$ of the metal does have a mass of $8.35\ \text{g}$ (from density). So the error is the kg - g conversion factor is upside down.

Answer:

The kg to g conversion factor is upside down