1. Converting Metric Units

2. Converting Metric Units
Common Metric Measurements
Distance
Mass
Capacity
1 km = 1,000 m
1 kg = 1,000 g
1 L = 1,000 mL
1 m = 100 cm
1 g = 1,000 mg
1 cm = 10 mm

3. Converting Metric Units
Here is an mnemonic to help you remember the order of the prefixes of the metric system.
BIGGER to Smaller
King Henry Doesn’t Usually Drink Chocolate Milk
ilo
ecto
eka
eci
enti
nit
illi
The “Unit” refers to when you are working with the pure unit – ex. - a meter or a liter.

4. Converting Metric Units
In the metric system, the value of each unit is 10 times greater than the value of the unit to its right. Therefore, when you want to convert one unit of measure to another, simply multiple or divide by a power of 10 (ex.: x 101, ÷ 102 or x 103) for each step that you take.
Multiply
Divide

5. Converting Metric Units
For the following conversions, indicate whether you would multiply or divide and by which amount you would multiply or divide.
1.) Grams to milligrams
2.) centiliters to kiloliters
3.) Millimeters to kilometers

6. Converting Metric Units
Using Powers of Ten
Example 1: The width of a book is about 22 centimeters. How many millimeters wide is the book?
Strategy:
* Find the metric unit that you are converting from and to.
* Determine what power of 10 you need to multiple or divide by.
* Multiply or divide by the correct power of 10.
** NOTE: You can also convert metric units by using conversion factors or proportions. **
22 cm = __ mm
22 • 101 =
22 • 10 = 22.0
220 mm
Original problem
Cm is one step larger than mm on the scale. Therefore, we will multiply 22 by 101 or 10.
Final answer
22 cm are equal to 220 mm.

7. Converting Metric Units
Using Powers of Ten
Example 2: A water bottle holds about 400 milliliters. How many liters of water does the bottle hold?
Strategy:
* Find the metric unit that you are converting from and to.
* Determine what multiple of 10 you need to power or divide by.
* Multiply or divide by the correct power of 10.
** NOTE: You can also convert metric units by using conversion factors or proportions. **
400 mL = __ L
400 ÷ 103 =
400 ÷ 1,000 =
0400.
0.4 L
Original problem
mL is three steps smaller than L. Therefore, we will divide 400 by 103 or 1,000.
Final answer
400 mL are equal to 0.4 L.

8. Converting Metric Units
Comparing Different Units
Example 3: Compare 5.2 kg to 60 g.
5.2 kg __ 60 g
5.2 • 103 =
5.2 • 1,000 = 5.200
5,200 g
Original problem
Strategy:
* Determine which unit you want both measurements to have.
* Then, convert both measurements to the same unit.
* Compare the measurements and place the correct symbol between them.
kg is three steps larger than g. Therefore, we will multiply 5.2 by 103 or 1,000.
Final answer
Conclusion: 5.2 kg = 5,200 g
Therefore, 5.2 kg. _>_ 60 g.

9. Converting Metric Units
Try these: Convert the measurements listed below using powers of ten.
1.) A desk is 60 centimeters wide. How many meters wide is the desk?
2.) A ball of clay has a mass of 4 kg. What is the mass of the clay in hectograms?

10. Converting Metric Units
Try these: Convert the measurements listed below using powers of ten.
3.) A bottle of water contains 0.8 L. How many mL does the bottle hold?
4.) A room is 8.2 meters wide. How wide is the room in decimeters?

11. Converting Metric Units
Real-Life Application
The Eurostar is a high-speed train that can travel up to 300 km/hr. The train travels from London to Paris under the English Channel. The distance between the two cities is 495 km. How many meters is this distance?