We need a reliable We need a reliable system of system of

measurementmeasurement to to obtain useful data.obtain useful data.

Before standardized units:Before standardized units:

Measurement used to be subjectiveMeasurement used to be subjective– One “foot” really was the length of a One “foot” really was the length of a

human foot. Obviously, foot size varies.human foot. Obviously, foot size varies.

In order to have consistency, there is In order to have consistency, there is a need for a a need for a standardizedstandardized system of system of units.units.– One foot should be the same length for One foot should be the same length for

every person.every person.

International System (S.I.) of International System (S.I.) of Units:Units:

Developed in the late 1700sDeveloped in the late 1700s You may recognize as the “Metric” system.You may recognize as the “Metric” system. Our “English” system was eventually Our “English” system was eventually

standardized also, but the S.I. system is standardized also, but the S.I. system is used by most countries and the used by most countries and the international scientific community.international scientific community.– We will use the S.I. system in class.We will use the S.I. system in class.– Based on 10– What is English system based Based on 10– What is English system based

on?on?

S.I. Base Units:S.I. Base Units: Base units can be measured directly.Base units can be measured directly.

Units for other measurements are Units for other measurements are calculatedcalculated from base units. from base units.

**One meter is equal to approximately 3 feet, 3 One meter is equal to approximately 3 feet, 3 inches.inches.

Measurement S.I. Unit S.I. Abbrev.

length meter m

mass gram g

time second s

temperature Kelvin, deg. Celsius K, °C

PrefixesPrefixes

kilo- (k), 1000 timeskilo- (k), 1000 times centi- (c), 1/100centi- (c), 1/100th th (There are 100 cents (There are 100 cents

in one dollar.)in one dollar.) milli- (m), 1/1000milli- (m), 1/1000thth

Example:Example: 1 km = 1000 meters1 km = 1000 meters 1 cm = 0.01 meter (100 cm = 1 m)1 cm = 0.01 meter (100 cm = 1 m) 1 mm = 0.001 meter (1000 mm = 1 1 mm = 0.001 meter (1000 mm = 1

m)m)

What does this mean?What does this mean? 1 kilometer (km) is approximately 0.6 1 kilometer (km) is approximately 0.6

milesmiles

1 meter (m) is approximately the 1 meter (m) is approximately the length from your fingertips to your length from your fingertips to your opposite shoulderopposite shoulder

1 centimeter (cm) is approximately the 1 centimeter (cm) is approximately the width of the tip of your pinkywidth of the tip of your pinky

2.54 cm = 1 inch2.54 cm = 1 inch

1 millimeter (mm) is approximately the 1 millimeter (mm) is approximately the width of a paperclip width of a paperclip wirewire

Is this a ridiculous speed limit sign?Is this a ridiculous speed limit sign? What does it mean?What does it mean? 120 km/h = 75 mi/h120 km/h = 75 mi/h

How do they fit together?How do they fit together?

10 mm = 1 cm10 mm = 1 cm100 cm = 1 m100 cm = 1 m

1000 m = 1 km1000 m = 1 km

Converting units:Converting units: Convert 1 km to centimeters.Convert 1 km to centimeters.

Known: 1 km = 1000 m, 1 m = 100 cmKnown: 1 km = 1000 m, 1 m = 100 cm

Therefore, 1000 m = 1 and 100 cm = 1Therefore, 1000 m = 1 and 100 cm = 1 1 km1 km 1 m 1 m

1 km x 1000 m x 100 cm = 100,000 1 km x 1000 m x 100 cm = 100,000 cmcm

1 km1 km 1 m 1 m

1 km 1000 m 100 cm = 100,000 cm1 km 1000 m 100 cm = 100,000 cm 1 km1 km 1 m 1 m

Mass is a measure of the amount of matter Mass is a measure of the amount of matter (stuff) that something is made of.(stuff) that something is made of.

Would you expect an elephant or a mouse to have a greater Would you expect an elephant or a mouse to have a greater mass?mass?

An elephant is made of a greater An elephant is made of a greater amount of stuff and, therefore,amount of stuff and, therefore,has a greater mass.has a greater mass.

In this class we will measure mass in In this class we will measure mass in grams or kilogramsgrams or kilograms..The mass of a penny is about 2 ½ to 3 grams.The mass of a penny is about 2 ½ to 3 grams.The mass of your teacher is about 50,000 grams (50 kg).The mass of your teacher is about 50,000 grams (50 kg).The mass of an elephant is about 5,000,000 grams (5,000 The mass of an elephant is about 5,000,000 grams (5,000 kg).kg).

Are mass and weight the same? We will compare mass and Are mass and weight the same? We will compare mass and weight later.weight later.

However, we measure mass with the same equipment we However, we measure mass with the same equipment we use to measure weight– a scale or “beam balance”.use to measure weight– a scale or “beam balance”.

VB-302-3000 Electronic Precision Balance Scale [Online]. Flex Weigh Direct 2006-07.

http://www.flexweighdirect.com/vb3023000/

The mass of this object is 2000 grams.

S.I. Derived UnitsS.I. Derived Units Derived units are combinations of base Derived units are combinations of base

units.units. Measurements of size:Measurements of size:

– LengthLength is a 1-dimensional is a 1-dimensionalsize measured insize measured inmeters (m) meters (m) base unit. base unit.

– AreaArea is a 2-dimensional size is a 2-dimensional sizemeasured inmeasured insquare meters (msquare meters (m22).).

– VolumeVolume is a 3-dimensional is a 3-dimensionalsize measured insize measured incubic meters (mcubic meters (m33).).

– Area and volume areArea and volume aregiven in given in derivedderived units. units.

3 m

3 m

3 m

3 m

3 m

3 m

The length of this line = 3 m.

The area of this square = 3 m x 3 m = 9 m2.

The volume of this cube =3 m x 3 m x 3m = 27 m3.

What is the area of a sheet of computer What is the area of a sheet of computer paper?paper?Area is a 2-dimensional measurement.Area is a 2-dimensional measurement.

Area = length x widthArea = length x width

Area = 0.22 m x 0.28 mArea = 0.22 m x 0.28 m

Area = 0.062 mArea = 0.062 m22

Square meters are aSquare meters are a

combination of meterscombination of meters

(meters x meters) (meters x meters) derived unit.derived unit.

0.22 m

0.2

8 m

Volume is a measure of the amount of space Volume is a measure of the amount of space something occupies or contains.something occupies or contains.

Imagine a pool ball and a tennis ball.Imagine a pool ball and a tennis ball.Compare the mass and volume of the two objects.Compare the mass and volume of the two objects. The two objects occupy approximately the same The two objects occupy approximately the same

amount of space and so have approximately equal amount of space and so have approximately equal volumes.volumes.

The pool ball has a much greater mass than the tennis The pool ball has a much greater mass than the tennis ball, as you can tell when you pick up the two objects.ball, as you can tell when you pick up the two objects.

Compare the mass and volume of a basketball and a Compare the mass and volume of a basketball and a bowling ball.bowling ball.

We use We use volumevolume measurements everyday. measurements everyday.

Example: The gas tank in my car contains Example: The gas tank in my car contains 15 gallons15 gallons of gasoline (when it is full). of gasoline (when it is full).

Example: A bread recipe calls for Example: A bread recipe calls for 2 cups2 cupsof water and of water and 3 tablespoons3 tablespoons of oil. of oil.

In science class, the In science class, the unitunit we will we willuse to measure the volumes ofuse to measure the volumes ofliquids is the liquids is the liter (L)liter (L)..

Think of the amount of spaceThink of the amount of spaceoccupied by a 1-liter or 2-literoccupied by a 1-liter or 2-literbottle of soda.bottle of soda.

The equipment we will use to measure The equipment we will use to measure liquidliquid volume in volume in class will be the class will be the beakerbeaker and the and the graduated cylindergraduated cylinder..

BeakersBeakers are generally are generallyused to measure largerused to measure largervolumes. They do notvolumes. They do nothave many markings.have many markings.

250 ml Bomex Glass Beaker [Online]. Research Laboratory Supply, Inc. 2008.Researchsupply.net

Graduated Cylinder, Glass, 50 ml [Online]. Science Stuff, Inc. 2008. Sciencestuff.com.

Graduated cylindersGraduated cylinders get their get their name from many small markings name from many small markings (similar to a ruler) that are used to (similar to a ruler) that are used to take a wide variety of large and take a wide variety of large and small measurements.small measurements.

What volume of water does an What volume of water does an Olympic-sized swimming pool Olympic-sized swimming pool contain?contain?Volume is a 3-dimensional Volume is a 3-dimensional measurement.measurement.

Volume = length x width x height Volume = length x width x height (depth).(depth).

Since area = length x width,Since area = length x width,

then volume = area x height.then volume = area x height.width = 25 m length = 50

m

depth = 2 m

Volume = l x w x d

Volume = 50 m x 25 m

x 2 m

Volume = 2500 m3

25 m

2 m

50

m

Volume = 2 m x 25 m x 50 m

Volume = 2500 m3

This volume is equivalent to2500 cubes of 1 m3

(1 m x 1 m x 1 m)

So is volume measured in cubic So is volume measured in cubic meters (mmeters (m33) or in liters (L)?) or in liters (L)?

Solids measured in mSolids measured in m33 only. only.

Liquids and gases measured in mLiquids and gases measured in m33 or L. or L.

What is the connection?What is the connection?1 cm1 cm33 = 1 mL = 1 mL for liquids and gases for liquids and gases

This is the This is the conversion factorconversion factor, which , which allows us to convert a measurement allows us to convert a measurement from one type of units to another.from one type of units to another.