5.1

Basic Terms and Conversions within the Metric System

SI System and U.S. Customary System

Most countries of the world use the Systéme international d’unités or SI system.

The SI system is referred to as the metric system in the United States.

Two systems of weights and measures exist side by side in the United States today, U.S customary system and the metric system.

Advantages to Using the Metric System

The metric system is the worldwide accepted standard measurement system.

There is only one unit of measurement for each physical quantity.

The SI system is based on the number 10, allowing less need for fractions.

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

AbbrevMetric Term

Metric Prefixes

1/1000 of base unitmmilli1/100 of base unitccenti1/10 of base unitddeci

base unit10 x base unitdadeka

100 x base unithhecto1000 x base unitkkilo

MeaningSymbolPrefix

Changing Units within the Metric System

To change from a smaller unit to a larger unit move the decimal point in the original quantity one place to the left for each larger unit of measure until you obtain the desired unit of measure.

To change from a larger unit to a smaller unit, move the decimal point in the original quantity one place to the right for each smaller unit of measurement until you obtain the desired unit of measure.

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

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

5.2

Length, Area, and Volume

Length

The meter is used to measure things that we normally measure in yards and feet.

Centimeters and millimeters are used to measure what we normally measure in inches. A centimeter is a little less than a half of an

inch. A millimeter is about the thickness of a dime.

Example: The length of a pair of scissors would be measured in centimeters.

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 x width.

A = 82.5 25.4A = 2095.5 m2

Volume

When a figure has three dimensions; length, width and height, the volume can be found.

The volume of an item can be considered the space occupied by the item.

Volume can be expressed in terms of liters or cubic meters.

1 m3 = 1 kL 1 dm3 = 1 L 1 cm3 = 1 mL

Volume in LitersVolume in Cubic Units

Volume

When the volume of a liquid is measured, the abbreviation cc is often used instead of cm3 to represent cubic centimeters.

Example: An asthma patient must mix 0.25 cc of a bronchodilator with 2 cc of saline to use in an aerosol machine.

How many milliliters of the bronchodilator will be administered?

What is the total volume of drug and saline solution in milliliters?

Volume continued

Solution: Since 1 cc is equal in volume to 1 milliliter,

there will be 0.25 milliliters of the bronchodilator.

The total volume is 0.25 + 2 or 2.25 cc, which is equal to 2.25 mL.

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

5.3

Mass and Temperature

Mass

Although weight and mass are not the same, on Earth they are proportional to each other. Mass is a measure of the amount of matter in

an object. Weight is the measure of gravitational pull on

an object.

Metric System

The kilogram is the basic unit of mass in the metric system. Example: A man has the mass of about 75 kg.

The gram is relatively small and used in place of the ounce. Example: A nickel has the mass of about 5 g.

The milligram is used in the medical and scientific fields.

The metric tonne (t) is used to express mass of heavy items. One metric tonne = 1000 kg.

Example: Choosing an Appropriate Unit

Determine which metric unit you would use to express the mass of the following.

a) A spider c) A bicycle b) A nickel d) A box of cereal

Example: Choosing an Appropriate Unit

Determine which metric unit you would use to express the mass of the following.

a) A spider c) A bicycle b) A nickel d) A box of cereal

Solution: a) Milligrams c) Kilograms b) Grams d) Grams

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 = 1 g

Mass of WaterVolume 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 continued

Solution:

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 h10.26 0.60.156 m3

Temperature

The term degrees Celsius (ºC) is used to measure temperature.

Water boils212ºF100ºC

Body temperature98.6ºF37ºC

Comfortable room71.6ºF22ºCWater freezes32ºF0ºC

DescriptionºFºCTemperature

Example: Choose ºF or ºC

The temperature of a can of frozen juice is about 2 __.

The temperature of a person with a fever is about 101.5 __.

The temperature of a bowl of hot soup is about 175 __.

Example: Choose ºF or ºC

The temperature of a can of frozen juice is about 2 __.

The temperature of a person with a fever is about 101.5 __.

The temperature of a bowl of hot soup is about 175 __.

Solution: a) ºC b) ºF c) ºF

Conversions

To convert from Celsius to Fahrenheit use the following formula.

To convert from Fahrenheit to Celsius use the following formula.

F

95

C 32 C

59

F 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 59

F 32

C 59

85 32

C 59

53 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 95

C 32

F 95

5 32

F 9 32F 41

5.4

Dimensional Analysis and Conversions to and from the

Metric System

Dimensional Analysis

Dimensional analysis is a procedure used to convert from one unit of measurement to a different unit of measurement.

A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1.

Examples of unit fractions:

16 oz1 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 pounds1 hour = 60 minutes1 pound = 16 ounces

1 minute = 60 seconds1 mile = 5280 feet1 gallon = 4 quarts1 yard = 3 feet1 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:

Convert 75 miles per hour to inches per minute.Solution:

8 cups = 8 cups 1 pint

2 cups

4 pints

75mihr

75mihr

5280ft1 mi

12 in1 ft

1 hr60 min

75 5280 12

60in

min = 79,200

inmin

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:

14.25 in2 6.5 cm2

1 in2

92.625 cm2

lgallgal 88.858.36.22

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 mi1.6 km

621.6

mi 38.75 mi

Example: Weight (Mass) Conversion for Medication

A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given?

Solution:

The dosage of the medication is 73.92 mg.

8 lbs 16 oz1 lb

4 oz 128 oz 4 oz 132 oz

132 oz28 goz

1 kg1000 g

20 mg1 kg

73.92 mg