Unit 5: The Metric System

The Metric System is used everywhere except Burma, Liberia, and U.S.A.

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 Metric

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 and complicated conversions.

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 unitddecibase unit10 x base unitdadeka100 x base unithhecto1000 x base unitkkiloMeaningSymbolPrefix

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 SystemMeasurement

Kilo-meter

Hecto-meter

Deka-meter

MeterDeci-

meterCenti-meter

Milli-meter

Symbol km hm dam m dm cm mm

Number of Meters 1000 100 10 1 0.1 0.01 0.001

Example: Changing Units

Convert 54.6 m to km. Convert 15 L to mL. Convert 0.89 kg to cg – Poll!

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?

Many prefixes!

Length, Area, and Volume

LengthThe 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.

AreaArea (of any shape) is 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.Area of a rectangle= length width.

VolumeWhen 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 drug with 2 cc of saline to use in an aerosol machine.

How many milliliters of the drug will be administered?

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

Volume continuedSolution: 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: Finding the volume A cylindrical shampoo bottle has a diameter of 6 cm and a height

of 12 cm. What is the volume in milliliters? (Use V = πr²h for the volume of a cylinder.)

Solution:

Mass and Temperature

MassAlthough weight and mass are not the same,

on Earth they are proportional to each other, so we can treat them as the same thing.

Mass is a measure of the amount of matter in an object.

Weight is the measure of gravitational pull on an object.

Metric SystemThe kilogram is the basic unit of mass in the

metric system. One kilogram weighs a bit more than 2 pounds.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.

Metric System

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 best express the mass of the following. a) A spider c) A bicycle b) A nickel d) A box of cereal

Solution: a) c) b) d)

Volume and Mass of WaterVolume 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: CapacityA 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.

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

Water boils212ºF100ºC

Body temperature98.6ºF37ºC

Mild spring day68ºF20ºC

Water freezes32ºF0ºC

DescriptionºFºC

Temperature

Example: Choose °F or °C The temperature of Chicago on a

summer day is about 35 __. The temperature of a person with a

fever is about 101.5 __. The temperature of cookies baking in

the oven is 175 __.

Solution: a) b) c)

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 85°F. What is the equivalent temperature on the Celsius thermometer?

Solution:

The equivalent temperature is about ____°C.

Example: Conversions The temperature of

a cold glass of milk is about 5°C . What is the equivalent temperature on the Fahrenheit thermometer?

Solution:

The equivalent

temperature is about

_____°F.

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 oz

1 lb

1 hr

60 min

12 in.

1 ft

U.S. Customary Units

1 pint = 2 cups 1 year = 365 days

1 cup (liquid) = 8 fluid ounces

1 day = 24 hours1 ton = 2000 pounds

1 hour = 60 minutes1 pound = 16 ounces

1 minute = 60 seconds1 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:

Convert 75 miles per hour to kilometers per hour.

Solution:

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:

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.

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.

Unit 6: Geometry!