Welcome to a lesson on comparing measurements given in metric units. In
the first example, if a person's pupillary distance, which is the distance
from one pupil to the other, is sixty-one millimeters, and the distance from their
pupil to the middle of their upper lip is seven centimeters, which distance is longer?
To answer this question, we need to compare the distances of sixty-one millimeters and seven
centimeters. And therefore, we need to convert sixty-one millimeters to centimeters,
or convert seven centimeters to millimeters.
For this example, we will convert seven centimeters to millimeters. We'll perform
the conversion using a unit fraction. So we'd first write seven centimeters as a
fraction with the denominator of one.
Now we multiply by a unit fraction that will convert centimeters to millimeters.
Looking at the conversions below, we will use the conversion, one centimeter equals
ten millimeters to form the unit fraction. Because we want centimeters to simplify
out of this product,
the units of centimeters must be in the denominator of the unit fraction, leaving
millimeters for the numerator. Now using the conversion, one centimeter equals ten
millimeters, the unit fraction is ten millimeters divided by one centimeter. This fraction
is equal to one, so we are not changing the value, we are changing the units by
multiplying by this fraction. Notice the units of centimeters simplify to one,
leaving us with the product of seven times ten millimeters, or seventy millimeters.
Because seven centimeters equals seventy millimeters, we answer the question by
comparing sixty-one millimeters
to seventy millimeters. Well because sixty-one millimeters is less than seventy millimeters,
we now know that sixty-one millimeters is less than seven centimeters. And therefore, seven
centimeters is the longer distance. When giving the answer
we give the distance using its original units. And therefore, we say the distance
of seven centimeters is longer than sixty-one millimeters.
Let's look at the second question.
One doctor purchased two thousand individual two point five grams doses of medication.
Another doctor purchased four point five kilograms of the same medication. Which
amount is more? To answer this question we need to compare two thousand, two point five gram
doses to four point five kilograms.
Well two thousand individual two point five gram doses would be two thousand
times two point five grams.
We want to compare this amount to four point five kilograms.
Well two thousand times two point five is five thousand, which means we compare five thousand grams
to four point five kilograms. And therefore, we need to convert five thousand grams to kilograms,
or four point five kilograms to grams. For this example we will convert five
thousand grams to kilograms using a unit fraction. Beginning with five thousand
grams as a fraction. With the denominator of one, we multiply by a unit fraction that
will convert grams to kilograms.
Looking at the conversions,
one kilogram is equal to one thousand grams.
We will use this conversion to form the unit fraction. We want grams to simplify
out of this product and therefore, grams must be in the denominator of the unit
fraction leaving kilograms for the numerator. The conversion is one kilogram
equals one thousand grams and therefore, the unit fraction is one kilogram divided by one thousand.
grams. The units of grams simplify to one.
The product gives us five thousand divided by
one thousand kilograms. Five thousand divided by one thousand is five and therefore, five thousand grams equals five
kilograms. So to compare five thousand grams and four point five kilograms,
we now compare five kilograms to four point five kilograms.
Well five kilograms is greater than four point five kilograms and therefore, five thousand
grams is greater than four point five kilograms. And now we know two thousand doses of two point five grams is
greater than four point five kilograms.
So we'll state, two thousand individual two point five grams doses is more than four point
five kilograms of the same medication.
I hope you found this helpful.