Objectives - Express lengths, mass, time in SI units. - SI metric system - Convert distances between different units. - Describe time intervals in hours,

Objectives- Express lengths, mass, time in SI units.- SI metric system - Convert distances between different units. - Describe time intervals in hours, minutes, and seconds. - Convert time in mixed units to time in seconds. - Describe the mass of objects in grams and kilograms.

Unit I Units and Measurement

It All Starts with a Ruler!!!

I. Two Systems of Units

a. Metric system and International System of Units

meter

kilogramsecondKelvin

b. English system inches, feet, yards, and miles.

pound Fahrenheit

meter (m): unit of length

kilogram (kg): unit of mass

second (s): unit of time

II. SI units

 meter, (SI unit symbol: m), is the fundamental unit of length in the International System of Units (SI).

Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level).

Since 1983, it has been defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."

National Prototype Metre Bar ( alloy of ninety percentplatinum and ten percent iridium) in  International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France.

 kilogramme ( kg), is the base unit of mass in the International System of Units (SI)

Is defined as being equal to the mass of the International Prototype of the Kilogram (platinum–iridium alloy) in International Bureau of Weights and Measures in Sèvres, France

Second (sec or s) The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

1. SI UNITS (Systéme Internationale)

Examples

The units for length, mass, and time (as well as a few others), are regarded as base SI units.

These units are used in combination to define additional units for other important physical

quantities such as force and energy.

2. SI base unitsUnit

nameUnit

symbolQuantity

nameDefinition (incomplete)[n 1] Dimension

symbol

metre m length

•Original (1793): 1/10000000 of the meridian through Paris between the North Pole and the Equator.FG

•Interim (1960): 1650763.73 wavelengths in a vacuum of the radiationcorresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.•Current (1983): The distance travelled by light in vacuum in 1/299792458second.

L

kilogram[n 2] kg mass

•Original (1793): The grave was defined as being the weight [mass] of one cubic decimetre of pure water at its freezing point.FG

•Current (1889): The mass of the international prototype kilogram.

M

second s time

•Original (Medieval): 1/86400 of a day.•Interim (1956): 1/31556925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.•Current (1967): The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of theground state of the caesium 133 atom.

T

ampere A electric current

•Original (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius creates a field of one oersted at the centre.[39] IEC

•Current (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length.

I

kelvin K thermodynamic temperature

•Original (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point of water and 100 °C to the boiling point of water.•Interim (1954): The triple point of water (0.01 °C) defined to be exactly 273.16 K.[n 3]

•Current (1967): 1/273.16 of the thermodynamic temperature of the triple point of water

Θ

mole mol amount of substance

•Original (1900): The molecular weight of a substance in mass grams.ICAW

•Current (1967): The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. [n 4]

N

candela cd luminous intensity

•Original (1946): The value of the new candle is such that the brightness of the full radiator at the temperature of solidification ofplatinum is 60 new candles per square centimetre.•Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012hertz and that has a radiant intensity in that direction of 1/683 watt persteradian.

J

Unitname

Unitsymbol

Quantityname Definition (incomplete)[n 1] Dimensionsymbol

3. The Metric System

• The metric system is a measurement system based on our decimal (base 10) number system.

• Other countries and all scientists and engineers use the metric system for measurement.

Metric Prefixes• Metric Units• The metric system has prefix modifiers that are multiples of

10.

Prefix Symbol Factor Number Factor Word

Kilo- k 1000 Thousand

Hecto- h 100 Hundred

Deca- da or dk 10 Ten

Unit m, l, or g 1 One

Deci- d .1 Tenth

Centi- c .01 Hundredth

Milli- m .001 thousandth

To change the scale of the base units, prefixes are attached. A prefix represents a factor by which the base unit must be multiplied. Metric prefixes are listed below (The prefixes most-commonly used in chemistry are listed in red):

Prefix Symbol Decimal Value Power of Ten

Exa- E 1,000,000,000,000,000,000 1018

Peta- P 1,000,000,000,000,000 1015

Tera- T 1,000,000,000,000 1012

Giga- G 1,000,000,000 109

Mega- M 1,000,000 106

Kilo- k 1,000 103

Hecto- h 100 102

Deka- da 10 101

(no prefix) 1 100

Deci- d 0 .1 10-1

Centi- c 0 .01 10-2

Milli- m 0 .001 10-3

Micro- µ 0 .000001 10-6

Nano- n 0 .000000001 10-9

Pico- p 0 .000000000001 10-12

Femto- f 0 .000000000000001 10-15

Atto- a 0 .000000000000000001 10-18

Place Values of Metric Prefixes

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkgkL

hmhghL

dkmdkgdkL

mgL

dmdgdL

cmcgcL

mmmgmL

Meters

• Meters measure length or distance

• One millimeter is about the thickness of a dime.

Meters• One centimeter is

about the width of a large paper clip

• or your fingernail.

Meters

• A meter is about the width of a doorway

Meters

• A kilometer is about six city blocks or 10 football fields.

• 1.6 kilometers is about 1 mile

Gram

• Grams are used to measure mass or the weight of an object.

Grams

• A milligram weighs about as much as a grain of salt.

Grams

• 1 gram weighs about as much as a small paper clip.

• 1 kilogram weighs about as much as 6 apples or 2 pounds.

Liters

• Liters measure liquids or capacity.

Liter

• 1 milliliter is about the amount of one drop

Liter

• 1 liter is half of a 2 liter bottle of Coke or other soda

Liter

• A kiloliter would be about 500 2-liter bottles of pop

1. By multiply or divide by a power of 10 – for unit change in metric system only• To change from one unit to another in the

metric system you simply multiply or divide by a power of 10.

III. THE CONVERSION OF UNITS

To change from a larger unit to a smaller unit, you need to multiply.

1 km x 1000 = 1000 m

1 m x 100 = 100 cm

1 cm x 10 = 10mm

Place Values of Metric Prefixes

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkLkg

hmhLhg

dkmdkLdkg

mLg

dmdLdg

cmcLcg

mmmLmg

Move the decimal point to the right to multiply.

Place Values of Metric Prefixes

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkgkL

hmhghL

dkmdkgdkL

mgL

dmdgdL

cmcgcL

mmmgmL

To change from smaller units to larger units you divide by a

power of ten.

1000mm ÷ 10 = 100cm

100cm ÷ 10 = 10dm

10dm ÷ 10 = 1m

Place Values of Metric Prefixes

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkLkg

hmhLhg

dkmdkLdkg

mLg

dmdLdg

cmcLcg

mmmLmg

Move the decimal point to the left to divide.

Place Values of Metric Prefixes

kmkgkL

hmhghL

dkmdkgdkL

mgL

dmdgdL

cmcgcL

mmmgmL

3km 30hm 300dkm 3000m

4L

30000dm 300000cm

12cm

3000000mm

2. The “Factor-Label” Method• Units, or “labels” are canceled, or

“factored” out

3

3

cm

gcm

33

cm

gcm g

• Regardless of conversion, keeping track of units makes things come out right

• Must use conversion factors• - The relationship between two units

• Canceling out units is a way of checking that your calculation is set up right!

Factor Label Method:

Steps:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

example: write 254 cm in km unit

for 1 km=1000 m=1000m x=100000cm

• Lining up conversion factors:

• Multiply proper factor:254 cm = 254cm= 0.00254km

==1

Example 1: Convert 3m to cm

Given Conversion Factor

= 300cm

For meters to cancel out, meters in the conversion factor must be on the opposite side of the fraction (fence).

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

3m 100 cm1m

Multiply every number on top of the fence and divide by the bottom.

Example 2: Convert 1516 g to kg

conversion factor

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve

for variables in an algebraic formula.

1.516 kg

1516 g 1 kg

1000 g

Whiteboard Problem 1

• Convert 1200 cm to m.

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

Whiteboard Problem 2

• Convert 5200 mL to L.

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

Example 3: Convert 7200mm to km

7200 mm

= .0072 km

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent)

variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

10 mm 1 cm 1 km

100,000 cm

Whiteboard Problem 3

• Convert 3 m to mm.

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent)

variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

3. relation between different units

1 ft = 0.3048 m

1 mi = 1.609 km

1 liter = 10-3 m3

example: for 1 in=2.54 cm

• Lining up conversion factors:

1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

Common conversion factors• English Factor

– 1 gallon = 4 quarts 4 qt/gal or 1gal/4 qt– 1 mile = 5280 feet 5280 ft/1mile or 1 mile/5280 ft– 1 ton = 2000 pounds 2000 lb/1ton or 1 ton/2000 lb

• Common English to Metric • 1 liter = 1.057 quarts 1.057 qt/1L or 1 L/1.057 qt

or 0.946 L/1qt

• 1 kilogram = 2.2 pounds 2.2 lb/1kg or 1 kg/2.2 lb • or 0.454 kg/1lb• 1 meter = 1.094 yards 1.094 yd/1m or 1m/1.094 yd• or 0.917m/1yd• 1 inch = 2.54 cm 2.54 cm/inch or 1 in/2.54 cm

Non-Metric (English) Unit Conversions

• Common Conversion Factors– 5280 ft = 1 mile– 12 in = 1 ft– 1 mile = 1600 m– 1 in = 2.54 cm– 3 ft = 1 yard

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

English to Metric conversion factors

Example 4: Convert 2 miles to ft

= 10,560 ft

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent)

variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

2 mi 5280 ft

1 mi

Whiteboard Problem 4

• Convert 3.2 ft to inches.

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

Example 5: Convert 5 ft to cm

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

5 ft 12 in

1 ft2.54 cm1 in

= 152. 4 cm 

Whiteboard Problem 5

• Convert 50 inches to m.

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

Problems

1. Convert 45 inches to cm.

= 114.3 cm

2. Convert 8 m to inches.

=

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2

Solve for variables in an algebraic formula.

Example 1.1

Grandma traveled 27 minutes at 44 m/s.How many miles did Grandma travel?

44.3 miles

mile/min=1.64mile/min

27𝑚𝑖𝑛×1.64𝑚𝑖𝑙𝑚𝑖𝑛

=44.3𝑚𝑖𝑙𝑒𝑠

convert

Example 1 The World’s Highest Waterfall

The highest waterfall in the world is Angel Falls in Venezuela,with a total drop of 979.0 m. Express this drop in feet.

Since 3.281 feet = 1 meter, it follows that

(3.281 feet)/(1 meter) = 1 and (1 meter) / (3.281 feet)=1

For meter feet:

feet 3212meter 1

feet 281.3meters 0.979 Length

Convert 100km to miles

• A football field is 100 yards long.• What is this distance expressed in meters?

3. Summary

Reasoning Strategy: Converting Between Units

1. In all calculations, write down the units explicitly.

2. Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically.

3. Use the conversion factors in reference tables. Be guided by the fact that multiplying or dividing an equation by a factor of 1 does not alter the equation.

IV. time• Two ways to think about time:

– What time is it? • 3 P.M. Eastern Time on April 21, 2004,

– How much time has passed?• 3 hr: 44 min: 25 sec.

• A quantity of time is often called a time interval.

Converting Mixed Units

1. You are asked for time in seconds.2. You are given a time interval in mixed

units.1 hour = 3,600 sec 1 minute = 60 sec

3. Do the conversion:1 hour = 3,600 sec26 minutes = 26 × 60 = 1,560 sec

4. Add all the seconds:t = 3,600 + 1,560 + 31.25 = 5,191.25 sec

Time Units

E) Practice

Example 2 Interstate Speed Limit

Express the speed limit of 65 miles/hour in terms of meters/second.

Use 5280 feet = 1 mile and 3600 seconds = 1 hour and 3.281 feet = 1 meter.

s

m29

s 3600

hour 1

mile

1609m

hour

miles 6511

hour

miles 65 Speed

second

meters29 Speed

More practice

1. Convert 789 cm2 to m2

2. Convert 75.00 km/h to m/s

75.00 km x 1000 m x 1 h___ = 20.83m/s

h 1 km 3600 s

1m=100cm, 1m2=100cm *100cm=10000cm2

=0.0789