Question

What is the volume in liters of 1.000 oz, given that 1 L = 1.0567 qt and 1 qt = 32 oz (exactly)?

Short answer

The volume of 1.000 oz is 2.956 × L.

Step-by-step solution

Common conversion factor

A unit conversion factor is a ratio of two equivalent amounts expressed in different measuring units.

It is given that 1 L = 1.0567 qt and 1 qt = 32 oz.

Explanation

As conversion factors, we need to employ the equivalency "factoids. A factoid is an essential parameter, which includes the given units. Put the supplied unit in the denominator where it will cancel out.

\(\frac{{1\,oz}}{1} \times \frac{{1\,qt}}{{32\,oz}} = \frac{1}{{32}}qt.\)

Continuation

As it can be seen, "oz" on the top cancels "oz" in the bottom, leaving the equation with "qt." We can stop here because we've converted from oz to qt.But, that's not what the task demanded of us, so we need to locate another factoid, this one involving "qt."

HINT: There is a factoid regarding L and qt.

\(\frac{{1\,oz}}{1} \times \frac{{1\,qt}}{{32\,oz}} \times \frac{{1\,lt}}{{1.0567\,qt}} = \frac{1}{{32}}qt \times \frac{{1\,lt}}{{1.0567\,qt}}.\)

Calculation

Multiply all the numbers in the numerators, then divide by each number in the denominators:

\(\begin{array}{c}\frac{{1 \times 1\,}}{{32 \times 1.0567\,}}lt = 0.02956\,L\\ = 2.956 \times {10^{ - 2}}\;L.\\\end{array}\)