Question

1. choose the best answer. which conversion factor in the train track should marcus use so the units cancel out? \\(\frac{1\text{ oz}}{0.029\text{ l}}\\) \\(\frac{0.029\text{ l}}{1\text{ oz}}\\)

Explanation:

Step1: Understand Unit Cancellation

To cancel units, the unit we want to eliminate should be in the denominator of the conversion factor if it's in the numerator of the original quantity (or vice versa). Assume the original unit is ounces (oz) and we want to convert to liters (L) or vice versa. If we have a quantity in oz, to cancel oz, the conversion factor should have oz in the denominator.

Step2: Analyze the Options

• First option: $\frac{1\ \text{oz}}{0.029\ \text{L}}$ has oz in numerator, L in denominator. If original unit is L, this would cancel L, but if original is oz, it would not.
• Second option: $\frac{0.029\ \text{L}}{1\ \text{oz}}$ has oz in denominator. If original unit is oz (in numerator), multiplying by this factor will cancel oz (since $\text{oz} \times \frac{\text{L}}{\text{oz}} = \text{L}$), achieving unit cancellation.

Answer:

$\frac{0.029\ \text{L}}{1\ \text{oz}}$ (the second option, $\boldsymbol{\frac{0.029\ \text{L}}{1\ \text{oz}}}$)