the metric system chapter 5. basic terms a little more than a quart volumelliter about 2.2 pounds...
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The Metric System
Chapter 5
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Basic Terms
a little more than a quart
volumeLliter
about 2.2 pounds
masskgkilogram
a little more than a yard
lengthmmeter
Comparison to Customary
Common Use
Abbrev
Metric Term
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Metric Prefixes
1/1000 of base unitmmilli1/100 of base unitccenti1/10 of base unitddecibase unit10 base unitdadeka100 base unithhecto1000 base unitkkiloMeaningSymbolPrefix
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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
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Changing Units within the Metric SystemMeasure 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
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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, 0.0546 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
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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.
18,000
250= 72
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Area Areas are always expressed in square units.Example:The length of a rectangular park is 82.5 m, and
its width is 25.4 m. Find the area of the park.Solution: Area = length width.
A = 82.5 25.4
A = 2095.5 m2
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VolumeThree dimensions:
LengthWidth Height
1 m3 = 1 kL
1 dm3 = 1 L
1 cm3 = 1 mL
Volume in LitersVolume in Cubic Units
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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:
V r 2h
V 3.14 3 2 12
V 339.12 cm3
V 339.12 mL
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Volume and Mass of Water
Volume in Cubic Units
1 m3 = 1 kL = 1 t (1000 kg)
1 dm3 = 1 L = 1 kg
1 cm3 = 1 mL = 1g
Mass of Water
Volume in Liters
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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.
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Example: Capacity continuedSolution:
Since 1 m3 of water = 1 kL of water, 0.156 m3 = 0.156 kL, or 156 liters of water Since 1L = 1 kg, 156 L = 156 kg of water.
V l w h
10.26 0.6
0.156 m3
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ConversionsTo covert from
Celsius to Fahrenheit use the following formula.
To covert from Fahrenheit to Celsius use the following formula.
F
9
5C 32
C
5
9F 32
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Example: Conversions The air temperature on a warm summer day
is about 85ºF. What is the equivalent temperature on the Celsius thermometer?
Solution:
C 5
9F 32
C 5
985 32
C 5
953
C 29.4
The equivalent temperature is about 29.4ºC.
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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.
F 9
5C 32
F 9
55 32
F 9 32
F 41
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Dimensional AnalysisExamples of unit fractions:
16 oz
1 lb
1 hr
60 min
12 in.
1 ft
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U.S. Customary Units
1 pint = 2 cups 1 year = 365 days1 cup (liquid) = 8 fluid ounces
1 day = 24 hours1 ton = 2000 pounds
1 hour = 60 minutes1 pound = 16 ounces
1 minute = 60 seconds
1 mile = 5280 feet
1 gallon = 4 quarts1 yard = 3 feet
1 quart = 2 pints1 foot = 12 inches
U.S. Customary Units
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Example: Using Dimensional Analysis
A recipe calls for 8 cups of blueberries. How many pints is this?
Solution:
8 cups = 8 cups 1 pint
2 cups
4 pint s
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Conversion to and from the Metric System - Length
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)
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Conversion to and from the Metric System - Area
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)
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Conversion to and from the Metric System - Volume
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)
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Conversion to and from the Metric System - Volume
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)
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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)
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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 14.25 in2. What is its area in square centimeters?
Solution:
3.8 l
22.6 gal = 85.88 lgal
14.25 in2 6.5 cm2
1 in2
92.625 cm2
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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 38.75 mi, 62 kph is equivalent to 38.75 mph.
62 km
1 mi
1.6 km
62
1.6mi 38.75 mi