Question

a human head weighs 160 ounces. what is that weight in kilograms? analyze the work below.
1 lb = 16 oz
1,000 g = 1 kg
1 kg = 2.2 lb
student’s work:
\\(\frac{160\\ oz}{1} \times \frac{16\\ lbs}{1\\ oz} \times \frac{1\\ kg}{2.2\\ lbs} \approx 1,163.6\\)
what is the student’s error?
\\(\circ\\) the student forgot to multiply by \\(\frac{1000\\ g}{1\\ kg}\\).
\\(\circ\\) the student forgot to multiply by \\(\frac{1\\ kg}{1000\\ g}\\).
\\(\circ\\) the student multiplied by \\(\frac{16\\ lb}{1\\ oz}\\) instead of \\(\frac{1\\ lb}{16\\ oz}\\).
\\(\circ\\) the student multiplied by \\(\frac{1\\ kg}{2.2\\ lb}\\) instead of \\(\frac{2.2\\ lb}{1\\ kg}\\).

Explanation:

Step1: Identify correct oz to lb conversion

The correct conversion factor is $1\ \text{lb}=16\ \text{oz}$, so to convert ounces to pounds, we use $\frac{1\ \text{lb}}{16\ \text{oz}}$.

Step2: Analyze student's conversion factor

The student used $\frac{16\ \text{lbs}}{1\ \text{oz}}$, which inverts the correct factor, leading to an incorrect large value.

Step3: Verify other options are incorrect

The problem does not require gram conversions, so the first two options are irrelevant. The kg/lb factor the student used is set up correctly for converting pounds to kg, so the last option is wrong.

Answer:

The student multiplied by $\frac{16\ \text{lb}}{1\ \text{oz}}$ instead of $\frac{1\ \text{lb}}{16\ \text{oz}}$