Lesson Objectives
• Demonstrate an understanding of multiplication by powers of 10
• Demonstrate an understanding of division by powers of 10
• Learn how to build a metric conversion prefix chart
• Learn how to convert between metric units of measurement

## How to Convert between Metric Units of Measurement

In our last lesson, we learned how to convert between U.S. customary units of measurement. In this lesson, we will learn how to convert between metric units of measurement. Most people in the U.S. are not familiar with the metric system. This can make metric conversion a bit challenging at first. Once the terminology is learned, the process becomes a bit simpler.
Metric System Basic Units
Weight (Mass) Volume Length
gramlitermeter
In our table above, we can see the basic units for the metric system. These units are:
• meter - used for length
• gram - used for weight (mass)
• liter - used for volume
When we work with U.S. units, we are often converting between different unit names. These units are chosen based on the size of what's being described. As an example, suppose we had 14,000 pounds of rice. We could more easily say we had 7 tons of rice since 2000 pounds = 1 ton. When we work with the metric system, things are a lot easier. Instead of having different unit names, prefixes are added to the front of the basic unit to scale up or down. These prefixes are based on powers of 10:
Metric Prefixes
Prefix Meaning
kilo1000
hecto100
deka10
basic unit1
deci1/10 or 0.1
centi1/100 or 0.01
milli1/1000 or 0.001
We can place a prefix in front of the basic unit to scale up or down:
• 1 kilometer = 1000 meters
• 1 dekagram = 10 grams
• 1 centiliter = 0.01 liters
• 4 hectograms = 400 grams
• hecto means 100, 4 hectograms tells us we have 4 x 100 or 400 grams
• 9 centimeters = 0.09 meters
• centi means 0.01, 9 centimeters tells us we have 9 x 0.01 or 0.09 meters
How can we change 6000 grams (g) into kilograms (kg)? We could set up a unit fraction and perform the multiplication: $$6000 \text{g}\cdot \frac{1 \text{kg}}{1000 \text{g}}$$ Our unwanted units (g) will cancel and we can simplify: $$\require{cancel}\cancel{6000}6 \cancel{\text{g}}\cdot \frac{1 \text{kg}}{\cancel{1000}\cancel{\text{g}}}=6 \text{kg}$$ There is an easier method to employ when working with the metric system. Recall from our lesson on multiplying decimals that we can quickly multiply a number by 10 or a power of 10 by moving the decimal point one place to the right for each zero in the power of 10. Additionally, we learned in our dividing decimals lesson that we can quickly divide a number by 10 or a power of 10 by moving the decimal point one place to the left for each zero in the power of 10. In our example above, we realize the relationship is such that for every 1000 grams we have 1 kilogram. So to change between the two, we can divide 6000 by 1000 or move the decimal point in 6000. three places to the left (since there are 3 zeros in 1000):
6000. » 6. » 6
This tells us 6000 grams is equal to 6 kilograms.

### Metric Prefix Chart

We can use a prefix chart to make metric conversion very simple. When we change between metric units, we are essentially just multiplying or dividing by the appropriate power of 10. Each time we move right on the prefix chart we are dividing by 10 and each time we move left we are multiplying by 10. The prefix chart allows us to match the movement on the chart with the movement of the decimal point in the number. Let's look at a sample prefix chart:

### King Henry Died Monday Unexpectedly Drinking Chocolate Milk

Typically we use "King Henry Died Unexpectedly Drinking Chocolate Milk" to remember the prefix chart:
• King » kilo
• Henry » hecto
• Died » deka
• Unexpectedly » unit (gram, meter, liter)
• Drinking » deci
• Chocolate » centi
• Milk » milli
In our above example, we went from 6000 grams to kilograms. We would identify kilo and our basic unit gram on the prefix chart: Since we are moving from the basic unit (gram) to kilogram, we will be dividing by 1000 or moving 3 places left on our prefix chart: When we match this movement in our number 6000, we end up with 6. This is how we quickly change between 6000 grams and 6 kilograms. Let's look at some examples.
Example 1: Change 47 centimeters to hectometers.
Let's look at our metric prefix chart: We can see that moving from centi to hecto on our prefix chart gives us a movement of 4 units left. We will match this movement with our number:
47. » 0.0047
47 centimeters = 0.0047 hectometers.
Example 2: Change 3.905 dekaliters to deciliters.
Let's look at our metric prefix chart: We can see that moving from deka to deci on our prefix chart gives us a movement of 2 units right. We will match this movement with our number:
3.905 » 390.5
3.905 dekaliters = 390.5 deciliters
Example 3: Change 0.591 kilograms to centigrams.
Let's look at our metric prefix chart: We can see that moving from kilo to centi on our prefix chart gives us a movement of 5 units right. We will match this movement with our number:
0.591 » 59,100
0.591 kilograms = 59,100 centigrams

#### Skills Check:

Example #1

Perform each conversion.

690.4 centimeters to decimeters

A
69.04
B
6.904
C
6,904
D
69,040
E
0.0694

Example #2

Perform each conversion.

22.6 decimeters to millimeters

A
2,260
B
22,260
C
2.26
D
0.0226
E
0.000226

Example #3

Perform each conversion.

9.61 hectograms to kilograms

A
961
B
0.961
C
96.10
D
9,610
E
961,000