Convert Metric Units to US Standard Units (Unit Fractions)
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Welcome to a lesson on converting metric units to U.S. standard units. For question a, the country of Cambodia is approximately seven hundred kilometers from north to south. What would this distance be in miles? We need to convert seven hundred kilometers to miles. We will perform the conversion using a unit fraction. To begin, we write seven hundred kilometers as a fraction with a denominator of one. And now we multiply by a unit fraction that will convert kilometers to miles. Looking at the conversions below for lengths, we are given zero point six two one miles equals one kilometer. We use this conversion to form the unit fraction. We want kilometers to simplify out of the product and therefore, kilometers must be in the
denominator of the unit fraction leaving miles for the numerator. Because zero point six two one miles equals one kilometer, the unit fraction is zero point six two one miles divided by one kilometer. Notice the units of kilometers simplify out, or simplify to one, leaving us with the product, seven hundred times zero point six two one miles, which equals four hundred thirty-four point seven miles. It is important to note that these conversions are only approximations and therefore, seven hundred kilometers is not exactly four hundred thirty-four point seven miles. This is actually just an approximation. But now we know seven hundred kilometers is approximately four hundred thirty-four point seven miles. For part b, we are asked to express five liters in terms of cups. We first write five liters as a fraction with a denominator of one. And now we multiply by unit fractions to convert liters to cups. Now looking at the conversions for volume. Notice how we are not given a conversion that relates liters to cups, which means, to perform the conversion we have to multiply by more than one unit fraction. We have a choice of using the conversion, one liter equals one point one quarts, or one liter equals two point one pints. Because pints are less than quarts and cups are less than pints, let’s use this conversion here to form the first unit fraction. We want liters to simplify out of the product and therefore, liters must be in the denominator of the first unit fraction. So pints will be in the numerator. The conversion, one liter equals two point one pints, and therefore, the unit fraction is two point one pints divided by one liter. The units of liters simplify out, or simplify to one, leaving us with pints. So now we convert pints to cups using the conversion, one pint equals two cups. We want pints to simplify out and therefore, pints must be in the denominator of this unit fraction, leaving cups in the numerator. Because the conversion is one pint equals two cups, the unit fraction is two cups divided by one pint. Now the units of pints simplify out, or simplify to one, leaving us with five times two point one, times two cups, which equals twenty-one cups. And again the conversion that we use to form this unit fraction is an approximation, so five liters is not exactly twenty-one cups and therefore, we will say five liters is approximately equal to twenty-one cups. I hope you found this helpful.

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