1. Chapter 5
The Metric System

2. Basic Terms a little more than a quart volume L liter about 2.2 pounds
mass kg
kilogram
a little more than a yard
length m
meter
Comparison to Customary
Common Use
Abbrev
Metric
Term

3. Metric Prefixes Prefix Symbol Meaning kilo k 1000  base unit hecto h
deka da
10  base unit
base unit
deci d
1/10 of base unit
centi c
1/100 of base unit
milli m
1/1000 of base unit

4. Changing Units within the Metric System
To change from a smaller unit to a larger unit move the decimal point to the left
To change from a larger unit to a smaller unit move the decimal point to the right

5. Changing Units within the Metric System
Measure of length
kilometer
hectometer
dekameter
Symbol km hm
dam
Number of meters
1000 m
100 m
10 m
Measure of length
meter
decimeter
centimeter
millimeter
Symbol m dm cm mm
Number of meters
1 m
0.1 m
0.01 m
0.001 m

6. Example: Changing Units
Convert 54.6 m to km.
Convert 15 L to mL.
Convert 0.89 kg to cg.
Solutions:
Meters is a smaller unit than km. Move the decimal 3 places to the left, km.
Liter is a larger unit than milliliter. Move the decimal point 3 places to the right, 15,000 mL.
Kilogram is a larger unit than centigram. Move the decimal point 5 places to the right 0.89 kg = 89,000 cg

7. Example: Application
A case of fruit juice contains twenty-four 0.75 liter bottles. How many 250 milliliter glasses can you fill using one case of juice? Solution: The case of juice contains 24(0.75) = 18 L. Converting 18 L = 18,000 mL. If each glass hold 250 mL, then glasses can be filled.

8. Area Areas are always expressed in square units. Example:
The length of a rectangular park is 82.5 m, and its width is m. Find the area of the park.
Solution: Area = length  width.

9. Volume 1 m3 = 1 kL 1 dm3 = 1 L 1 cm3 = 1 mL Volume in Liters
Three dimensions:
Length
Width
Height
1 m = kL
1 dm = L
1 cm = mL
Volume in Liters
Volume in Cubic Units

10. Example: Volume Application
A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters? Solution:

11. Volume and Mass of Water
Volume in Cubic Units
1 m = kL = 1 t (1000 kg)
1 dm = L = kg
1 cm = mL = g
Mass of Water
Volume in Liters

12. Example: Capacity A fish tank is 1 m long, 60 cm high and 260 mm wide.
Determine the number of liters that the tank holds.
What is the mass of the water in kilograms.

13. Example: Capacity continued
Solution:
Since 1 m3 of water = 1 kL of water,
0.156 m3 = kL, or 156 liters of water
Since 1L = 1 kg, 156 L = 156 kg of water.

14. Conversions
To covert from Celsius to Fahrenheit use the following formula.
To covert from Fahrenheit to Celsius use the following formula.

15. Example: Conversions The equivalent temperature is about 29.4ºC.
The air temperature on a warm summer day is about 85ºF. What is the equivalent temperature on the Celsius thermometer?
Solution:
The equivalent temperature is about 29.4ºC.

16. Example: Conversions
The temperature of a cold glass of milk is about 5ºC . What is the equivalent temperature on the Fahrenheit thermometer?
Solution:
The equivalent temperature is about 41ºF.

17. Dimensional Analysis
Examples of unit fractions:

18. U.S. Customary Units 1 pint = 2 cups 1 year = 365 days
1 cup (liquid) = 8 fluid ounces
1 day = 24 hours
1 ton = 2000 pounds
1 hour = 60 minutes
1 pound = 16 ounces
1 minute = 60 seconds
1 mile = 5280 feet
1 gallon = 4 quarts
1 yard = 3 feet
1 quart = 2 pints
1 foot = 12 inches
U.S. Customary Units

19. Example: Using Dimensional Analysis
A recipe calls for 8 cups of blueberries. How many pints is this?
Solution:

20. Conversion to and from the Metric System - Length
U.S. to Metric
1 inch (in.) ≈ 2.54 centimeters (cm)
1 foot (ft) ≈ 30 centimeters (cm)
1 yard (yd) ≈ 0.9 meter (m)
1 mile (mi) ≈ 1.6 kilometers (km)

21. Conversion to and from the Metric System - Area
U.S. to Metric
1 square inch (in.2) ≈ 6.5 square centimeters (cm2)
1 square foot (ft2) ≈ 0.09 square meter (m2)
1 square yard (yd2) ≈ 0.8 square meter (m2)
1 square mile (mi2) ≈ 2.6 square kilometers (km2)
1 acre ≈ 0.4 hectare (ha)

22. Conversion to and from the Metric System - Volume
U.S. to Metric
1 teaspoon (tsp) ≈ 5 milliliters (ml)
1 tablespoon (tbsp) ≈ 15 milliliters (ml)
1 fluid ounce (fl oz) ≈ 30 milliliters (ml)
1 cup (c) ≈ 0.24 liter (l)
1 pint (pt) ≈ 0.47 liter (l)

23. Conversion to and from the Metric System - Volume
U.S. to Metric
1 quart (qt) ≈ 0.95 liter (l)
1 gallon (gal) ≈ 3.8 liters (l)
1 cubic foot (ft3) ≈ 0.03 cubic meter (m3)
1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)

24. Conversion to and from the Metric System - Weight (Mass)
WEIGHT OR MASS
U.S. to Metric
1 ounce (oz) ≈ 28 grams (g)
1 pound (lb) ≈ 0.45 kilogram (kg)
1 ton (T) ≈ 0.9 tonne (t)

25. Example: Volume and Area
A gas tank holds 22.6 gallons of gas. How many liters is this?
Solution:
The area of a box is in2. What is its area in square centimeters?

26. Example: Converting Speed
A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour.
Solution:
Since 62 km equals mi, 62 kph is equivalent to mph.