Chapter 2Chapter 2

Measurements and CalculationsMeasurements and Calculations

Units of Measurements Units of Measurements Temperature:Temperature:

water water ooF F ooC C K K

boiling pt. boiling pt. 212 212 100 100 373.15 373.15

freezing freezing pt. pt.

32 32 0 0 273.15 273.15

absolute absolute zero zero

-459.67 -459.67 -273.15 -273.15 0 0

TemperatureTemperature

K = K = ooC + 273.15C + 273.15 ooF = (F = (ooC x 9/5) + 32C x 9/5) + 32 ooC = (C = (ooF – 32)/1.8F – 32)/1.8

Celsius, Fahrenheit, & Kelvin ScaleCelsius, Fahrenheit, & Kelvin Scale

Metric ConversionMetric Conversion

A measurement system based on 10A measurement system based on 10The official system used in the science The official system used in the science

community (IUPAC – international union of community (IUPAC – international union of pure and applied chemistry)pure and applied chemistry)

LENGTHLENGTH- (Meter) How far that light can - (Meter) How far that light can travel in a vacuum in 1/299,792,458 of a travel in a vacuum in 1/299,792,458 of a second. A platinum bar in France is used second. A platinum bar in France is used as the official length.as the official length.

Metric ConversionMetric Conversion

Volume Volume - (Liter) One - (Liter) One milliliter (1/1000 of a milliliter (1/1000 of a liter) was defined as liter) was defined as the amount of water the amount of water that would fill a box 1 that would fill a box 1 cm x 1 cm x 1 cm. cm x 1 cm x 1 cm. (1mL is also known (1mL is also known as a “cc” or cubic as a “cc” or cubic centimeter)centimeter)

1 cm

1 1 cmcm

1 cm1 cm

1 cm3 = 1 mL

Metric ConversionMetric Conversion

MassMass – (Gram) Defined as the mass of – (Gram) Defined as the mass of the water in that milliliter box at 4°C. the water in that milliliter box at 4°C.

TimeTime – (Second) There is only one timing – (Second) There is only one timing system so far.system so far.

PressurePressure – – Torr/ mmHgTorr/ mmHg The first scale for pressure. The first scale for pressure.

Torricelli of Italy made the first barometer and Torricelli of Italy made the first barometer and at sea level it made a column of mercury (Hg) at sea level it made a column of mercury (Hg) rise 760 mm high.rise 760 mm high.

AtmosphereAtmosphere This is a commonly used This is a commonly used system. 1 atmosphere is equal to 760 mmHg.system. 1 atmosphere is equal to 760 mmHg.

Pascal Pascal 1 atmosphere is equal to 101,300 1 atmosphere is equal to 101,300 pascalspascals

MEMORIZE:MEMORIZE:1 atm = 760 torr = 760 mmHg = 101,300 Pa = 1 atm = 760 torr = 760 mmHg = 101,300 Pa =

101.3 KPa101.3 KPa

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Metric Conversion Metric Conversion Terrible, Great and Majestic King Henry Terrible, Great and Majestic King Henry

Ducked Under Desks Counting Money Ducked Under Desks Counting Money Mighty Nice PlanningMighty Nice Planning

2.45 kg = g 2.45 kg = g 8.3 mm = dam8.3 mm = dam

mega = 106 micro = 10-6

giga = 109 nano = 10-9

tera = 1012 pico = 10-12

Scientific Notation Scientific Notation

value is expressed in the form:value is expressed in the form:

a.bbb x 10a.bbb x 10yy

where “a.” must be between 1 and 9where “a.” must be between 1 and 9

a.bbb = coefficienta.bbb = coefficient

X 10X 10 yy = base = base

y = exponenty = exponent

THIS MEANS YOU CAN ONLY HAVE ONE DIGIT IN-FRONT OF THE DECIMAL!!

WHAT DOES THE SIGN MEAN?WHAT DOES THE SIGN MEAN?

POSITIVE POSITIVE EXPONENTSEXPONENTS

When the exponent is When the exponent is positive the number will positive the number will be larger than 1be larger than 1

Ie. 450 or 6,000,000Ie. 450 or 6,000,000

We move the decimal the We move the decimal the number of times the number of times the exponent number isexponent number is

Ie. 3.72 x 10Ie. 3.72 x 1055

3 7 2 0 0 03 7 2 0 0 0

NEGATIVE NEGATIVE EXPONENTSEXPONENTS

When the exponent is When the exponent is negative the number negative the number will be smaller than 1will be smaller than 1

Ie. 0.3 or 0.0000820Ie. 0.3 or 0.0000820

We move the decimal the We move the decimal the number of times the number of times the exponent number isexponent number is

Ie. 9.32 x 10Ie. 9.32 x 10--7--7

0 0 0 0 0 0 0 0 9 3 2 0 0 0 0 0 0 9 3 2

When Converting a Decimal When Converting a Decimal NumberNumber

Number Larger than OneNumber Larger than One

Move the decimal until Move the decimal until only one digit is in-front only one digit is in-front of the decimal. This of the decimal. This number must be 1-9. number must be 1-9.

Move LeftMove Left

Ie. 28,765,300,000Ie. 28,765,300,000

2 .87653 x 102 .87653 x 101010

Number Smaller than OneNumber Smaller than One

Move the decimal until Move the decimal until only one digit is in-front only one digit is in-front of the decimal. This of the decimal. This number must be 1-9. number must be 1-9.

Move RightMove Right

Ie. 0.00000583Ie. 0.00000583

5 .83 x 105 .83 x 10--6--6

When the Exponent is ZeroWhen the Exponent is Zero Anything to the zero power is equal to Anything to the zero power is equal to

oneone

220 0 = 1= 1 5500 = 1 so… 10 = 1 so… 1000 = 1 = 1 Anything time one is equal to itself.Anything time one is equal to itself.

so..so..

4.7 x 104.7 x 100 0 4.7 x 1 4.7 x 1 4.7 4.7

Using your calculator for Using your calculator for Scientific NotationScientific Notation

You will be using the EE or EXP button You will be using the EE or EXP button on your calculator on your calculator

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2.3 x 102.3 x 108 8 // 4.2 x 10 4.2 x 1022 = =

1st- Input 1st- Input 2.32.3, Then push the EE button, then input the , Then push the EE button, then input the exponent of exponent of 88 (2.3 08) (2.3 08)

Now- Push the Divided by sign Now- Push the Divided by sign Next- Input Next- Input 4.24.2 , Then push the EE button, Then input the , Then push the EE button, Then input the

exponent of exponent of 22 (4.2 02) (4.2 02) Finally- Push the equals signFinally- Push the equals sign

Answer : 547619.0476 Answer : 547619.0476 5.48 x 105.48 x 1055

Now you try…Now you try…

( 9.65 x 10( 9.65 x 109 9 ) ( 3.20 x 10 ) ( 3.20 x 10 --3 3 ) / 8.11 x 10) / 8.11 x 104 4 ==

Did you get Did you get 380.76448 or 3.81 x 10380.76448 or 3.81 x 1022