The Metric System

Chapter 5

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

Metric Prefixes

1/1000 of base unitmmilli1/100 of base unitccenti1/10 of base unitddecibase unit10 base unitdadeka100 base unithhecto1000 base unitkkiloMeaningSymbolPrefix

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

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

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

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

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

VolumeThree dimensions:

LengthWidth Height

1 m3 = 1 kL

1 dm3 = 1 L

1 cm3 = 1 mL

Volume in LitersVolume in Cubic Units

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

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

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.

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

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

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.

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

Dimensional AnalysisExamples of unit fractions:

16 oz

1 lb

1 hr

60 min

12 in.

1 ft

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

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

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)

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)

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)

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)

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)

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

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