Basic Mathematics for College Students

5.4 Metric Units of Measurement 463

Self Check 7

MEDICATIONS A bottle of

Isoptin (a drug taken for high

blood pressure) contains

90 tablets, and each has 200 mg

of active ingredient, how many

grams of active ingredient are

in the bottle?

Now TryProblems 47 and 95

We can use the unit conversion factor method to confirm this result. To convert
to grams, we must chose a unit conversion factor such that the units of kilograms
drop out and the units of grams remain. Since there are 1,000 grams per 1 kilogram,
we multiply 7.86 kilograms by.

Simplify.

Multiply 7.86 by 1,000 by moving the

 7,860 g decimal point 3 places to the right.

 7.86#1,000 g

Remove the common units of kilograms in the

7.86 kg numerator and denominator. The units of g remain.

7.86 kg

1



1,000 g

1 kg

1,000 g

1 kg

EXAMPLE (^7) Medications A bottle of Verapamil, a drug taken for high
blood pressure, contains 30 tablets. If each tablet has 180 mg of active ingredient,
how many grams of active ingredient are in the bottle?
StrategyWe will multiply the number of tablets in one bottle by the number of
milligrams of active ingredient in each tablet.
WHYWe need to know the total number of milligrams of active ingredient in one
bottle before we can convert that number to grams.
Solution
Since there are 30 tablets, and each one contains 180 mg of active
ingredient, there are
5400.0 mg
of active ingredient in the bottle. To use a conversion chart to solve this problem,
we locate the original units of milligrams and then move to the conversion units of
grams, as shown below.
3 places to the left
We see that the decimal point in 5,400.0 should be moved 3 places to the left
to convert from milligrams to grams.
Move 3 places to the left.
There are 5.4 grams of active ingredient in the bottle.
We can use the unit conversion factor method to confirm this result. To
convert milligrams to grams, we multiply 5,400 milligrams by.
Multiply the fractions.
Divide 5,400 by 1,000 by moving the understood
 5.4 g decimal point in 5,400 three places to the left.



5,400

1,000

g

Remove the common units of milligrams

from the numerator and denominator.

The units of g remain.

5,400 mg

5,400 mg

1



1 g

1,000 mg

1 g

1,000 mg^

5,400 milligrams5.400  grams



kg hg dag g dg cg mg

30 #180 mg5,400 mg

180

 30

000

5400

5,400