Page 427 - Basic College Mathematics with Early Integers

404 C HAPTE R 5 I RATIO, PROPORTION, AND MEASUREMENT

from one unit of mass to another in the metric system, list the units of mass in order
from largest to smallest.
Let’s convert 4300 milligrams to grams.To convert from milligrams to grams, we
move along the list 3 units to the left.

kg hg dag g dg cg mg

3 units to the left
This means that we move the decimal point 3 places to the left to convert from
milligrams to grams.
4300 mg=4.3 g

Don’t forget, the same conversion can be done with unit fractions.
4300 mg 4300 mg 0.001 g
4300 mg = # 1 = #
1 1 1mg
#
= 4300 0.001 g
= 4.3 g To multiply by 0.001, move the decimal point 3 places to the left.
To see that this is reasonable, study the diagram:

1000 mg 1000 mg 1000 mg 1000 mg 300 mg

4300 mg
4.3 g

1 g 1 g 1 g 1 g 0.3 g
Thus, 4300 mg = 4.3 g .

PRACTICE 7 Example 7 Convert 3.2 kg to grams.
Convert 3.41 g to milligrams.
Solution: First we convert by using a unit fraction.
Unit fraction
2
1000 g
#
3.2 kg = 3.2 kg 1 = 3.2 kg # = 3200 g
1kg
Now let’s list the units of mass in order from left to right and move from kilograms
to grams.

kg hg dag g dg cg mg

3 units to the right
3.200 kg=3200. g
3 places to the right

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1 kg 1 kg 1 kg 0.2 kg

3.2 kg
3200 g

1000 g 1000 g 1000 g 200 g

Answer Work Practice 7
7. 3410 mg