 In this video, we will convert volume between metric and customary units. In this first example,
we’re asked to convert 3.5 kiloliters to quarts, using just the conversions provided below. Notice there’s only one conversion that converts from metric
to customary units, which is one liter is
approximately 0.26 gallons. Which means to convert
3.5 kiloliters to quarts, we will first have to
convert kiloliters to liters, then liters to gallons,
and then gallons to quarts. Because we have to use three conversions, we will multiply by three unit fractions. To set this up, we first
write 3.5 kiloliters as a fraction with a denominator of one, and then we’re going to multiply
by three unit fractions. We first convert kiloliters to liters because we want kiloliters to simplify out and right now we have
kiloliters in the numerator. For the first unit fraction, kiloliters must be in the denominator and liters in the numerator. And since one kiloliter is
equal to a thousand liters, the first unit fraction is
1,000 liters over one kiloliter. Notice how the units of
kiloliters simplify out because we have kiloliters
divided by kiloliters. And now let’s convert liters to gallons using this conversion. We want liters to simplify out and therefore liters must
be in the denominator and gallons in the numerator. And the conversion is one liter is approximately 0.26 gallons, which means the unit fraction is 0.26 gallons over one liter. And liters simplify out. Now that we have gallons,
we can convert to quarts using the conversion one
gallon equals four quarts. We want gallons to simplify out, and therefore gallons
must be in the denominator and quarts in the numerator. Since one gallon equals four quarts, the unit fraction is four
quarts over one gallon. Gallons simplify out,
leaving us with quarts. So now we need to find the product. And this will be an approximation because the conversion from liters to
gallons is an approximation. So going to the calculator, notice how the denominator is one and therefore the product
is 3.5 times 1,000, times .26 times four, which gives us approximately 3,640 quarts. For the second example, we want to convert six cups to milliliters. We begin by writing six cups as a fraction with a denominator of one. To perform this conversion,
we’ll have to use quite a few unit fractions. We will first convert cups to pints, then pints to quarts,
then quarts to gallons. Once we have gallons, we can
convert gallons to liters, and then finally liters to milliliters. Because we’ll have to
use five conversions, we will need five unit fractions. So one, two, three, four, and five. We first convert cups to pints. We want cups to simplify
out, and therefore cups must be in the denominator
and pints in the numerator. One pint equals two cups, and therefore the first unit fraction
is one pint over two cups. And cups simplify out. And now we convert pints to quarts. We want pints to simplify out. Pints must be in the denominator and quarts in the numerator. One quart equals two pints,
and therefore the unit fraction is one quart over two pints,
and pints simplify out. Now we convert quarts to gallons. We want quarts to simplify out. Quarts must be in the denominator and gallons in the numerator. One gallon equals four quarts. The unit fraction is one
gallon over four quarts and quarts simplify out. Now that we have gallons,
we can convert to liters using this conversion here. We want gallons to simplify out. Gallons must be in the denominator and liters in the numerator. Using the conversion, the unit fraction is one liter over 0.26 gallons. And gallons simplify out,
leaving us with liters. And finally we can convert to milliliters using the conversion one liter is equal to 1,000 milliliters. We want liters to simplify out. Liters must be in the denominator and milliliters in the numerator. And the unit fraction is 1,000
milliliters over one liter. And liters simplify out. So now we need to find the product. Notice in the numerator
we have six times 1,000. In the denominator we have two times two times four times 0.26. And of course now the
units are milliliters. So now we go back to the calculator. We need parentheses around
the numerator and denominator, so we have open parenthesis,
six times 1,000, close parenthesis, divided by, open parenthesis, two times
two times four times .26, close parenthesis, enter. Rounding to the tenths place value, we have approximately 1,442.3 milliliters. I hope you found this helpful.