Metric and US customary units, converting units

1. Measuring Matter
(and converting units)

2. English Metric

3. English
units – base 4
Metric
Units – base 10
12 inches to a foot
3 feet to a yard
1760 yards in a mile
2 cups in a pint
4 quarts in a gallon
16 ounces in a pound
2000 pounds in a ton
100 cm = 1 meter
1000 m = 1 kilometer
100 cL = 1 Liter
1000 L = 1 kiloliter
100 cg = 1 gram
1000 g = 1 kilogram

4. Metric System Units
• Base units for different measurements
• Length = meter (SI = m)
• Volume = liter (SI = m3
)
• Weight (Mass) = gram (SI = kg)
• Temperature = degrees Celsius (SI = K)

5. Metric System
• Scale is based on powers of ten:
– kilo (1000)
– centi (1/100)
– milli (1/1000)
kilo hecto deca
Base Units
meter
gram
liter
deci centi milli
1000 100 10 1 0.1 0.01 0.001

6. • meter is the base unit for length
– Length of a tree branch
• 1.5 meters
– Length of a room
• 5 - 10 meters
– Length of a ball of twine stretched out
• 25 - 50 meters

7. • What about a longer distance, like
from your house to school?
– Let’s say you live 10 miles
from school
• 10 miles = 16093 meters
– 16093 is a big number
– what if you could add a prefix onto the
base unit to make it easier to manage?
• 16093 meters = 16.093 kilometers
(or 16.1 if rounded to 1 decimal place)

8. • For each “step” to the right, you move the
decimal in the same direction
Example: change meters to centimeters
1 meter = 10 decimeters = 100 centimeters
or
1.00 meter = 10.0 decimeters = 100. centimeters
kilo hecto deca
meter
liter
gram
deci centi milli
Converting Units
(multiply method)
Converting Units
(decimal method)

9. Another Example
• Now let’s start from centimeters and convert
to kilometers
400,000 centimeters = 4.00000 kilometers
OR 4 km
kilo hecto deca
meter
liter
gram
deci centi milli

10. More Practice
• Now let’s start from meters and convert to centimeters
5 meters = 500 centimeters
kilo hecto deca
meter
liter
gram
deci centi milli
kilo hecto deca
meter
liter
gram
deci centi milli
• Now let’s start from kilometers and convert to meters
.3 kilometers = 300 meters

11. Experiment 23.1
Measuring Matter (ME!)
Type of
Measure
English
Units
Metric
Units
How tall are you? Length inches cm
How high can you jump?
How much do you weigh? Mass pounds kg
How strong is your hair?
For how long can you jump on one leg? Time min/sec s
How fast can you do 10 jumping jacks?
How much air do your lungs hold? Volume gallons l
How much can you swallow in one gulp?
How warm is it inside your ear? Temp. 0
F 0
C
How warm is the palm of your hand?

12. English Units
• The U.S. is one of only a few countries using the
"English Standard" or “customary” unit system
– inches/feet/yards (length)
– cups/quarts/gallons (volume)
– ounces/pounds (weight/mass)
– Fahrenheit (temperature)

13. • The “Factor-Label” Method
– Units are canceled or “factored” out
Example: convert yards to meters
Using Dimensional Analysis
to Convert English to Metric Units
meter
yards
xyards = meters
Start with what
you know
Multiply by the
conversion
factor
What unit you’re
trying to get to

14. Why Conversion Factors Work
• 5 x 2 = 5 x 1 =
2
• 3 x 0.7 = 3 x 1 =
0.7
• 6 x 0.5 = 6 x 1 =
½
5
3
6
• 4 ft x 12 in =
1 ft
• 150cm x 1m =
100 cm
• 2 m x 1 yd =
0.9 m
48 in
1.5m
2.2 yd

15. Conversion Factors

16. Dimensional Analysis
• Steps:
1. Identify begining & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units.
1 meter
1.1 yards
x5 yards = ? meters
1 1
2
5 x 1m
1.1
= 4.54 meters
3
4
4.56 m
Convert 5 yards into meters.