Question

1. clive is converting between units in the two measurement systems. his unit cancellation is shown below. what unit did he start with, and what unit did he end with? explain how you know.

\\( \frac { 3 \mathrm { lbs } } { 1 } \times \frac { 16 \mathrm { oz } } { 1 \mathrm { lb } } \times \frac { 28.350 \mathrm { g } } { 1 \mathrm { oz } } \\)

Explanation:

Step1: Analyze unit cancellation

In unit conversion, we multiply by conversion factors. The first factor is $\frac{3\ \text{lbs}}{1}$, then $\frac{16\ \text{oz}}{1\ \text{lb}}$, then $\frac{28.350\ \text{g}}{1\ \text{oz}}$. We cancel units: lbs cancel with lbs, oz cancel with oz.

Step2: Determine start and end units

The starting unit is the numerator of the first factor, which is pounds (lbs). After canceling, the remaining unit is grams (g), so the end unit is grams.

Answer:

He started with pounds (lbs) and will end with grams (g). This is because in the unit cancellation, pounds cancel out with the pounds in the denominator of the second factor, ounces cancel out with the ounces in the denominator of the third factor, leaving grams as the final unit. The calculation is a series of unit conversions: first converting pounds to ounces (using $1\ \text{lb} = 16\ \text{oz}$) and then ounces to grams (using $1\ \text{oz} = 28.350\ \text{g}$), so the overall conversion is from pounds to grams.