Updated Aug 2006Created by C. Ippolito August 2006 Measurement Objectives: list three requirements...

Created by C. IppolitoAugust 2006

Updated Aug 2006

MeasurementObjectives:

list three requirements for making a measurementexpress measurements in the International System of Units (SI)list the seven basic SI unitsbe able to combine SI units to form SI derived unitsdetermine the amount of uncertainty in a measured quantitycorrectly apply the terms accuracy and precisiondetermine the number of significant digits for a given calculation or measurementcalculate the percent error of an experimental result

Updated Aug 2006 Created by C. IppolitoAugust 2006

Chemical Quantities

• Chemistry– science that studies the structure and

nature of matter– describes characteristics or properties

of matter– QualitativeQualitative

• characteristics that can be described using words

– QuantitativeQuantitative• characteristics that can be measured and

described using a standard numerical unit


Measurements

• Requirements for Measuring1. know what is being measured

2. have a standard to compare measurement to

3. have a method of making comparison

• Measurements– comparison between quantity

measured and a standard unit


International System of Units

• International agreement– determined a set of standard units to be

used in scientific measurements– based on older French system used in

Europe– a.k.a. metric system

• advantages– calculations easier with use of decimals– units change from larger to smaller and

from smaller to larger in multiples of ten


SI Base Units

QuantityQuantity UnitUnit SymbolSymbol

length meter m

mass kilogram kg

time second s

amount of substance mole mol

temperature kelvin K

electric current ampere A

luminous intensity candela cd


SI Prefixes

• used with base units to form new units that are greater than or less than the base unit

• units increase or decrease by some multiple of 10


Prefixes for Greater Units

PrefixPrefix SymbolSymbol Multiply byMultiply by

exa- E 1 000 000 000 000 000 000

peta- P 1 000 000 000 000 000

tera- T 1 000 000 000 000

giga- G 1 000 000 000

mega- M 1 000 000

kilo- k 1 000

hecto- h 100

deca- da 10


Prefixes for Lesser Units

PrefixPrefix SymbolSymbol Multiply byMultiply by

deci- d 0.1

centi- c 0.01

milli- m 0.001

micro- μ 0.000 001

nano- n 0.000 000 001

pico- p 0.000 000 000 001

femto- f 0.000 000 000 000 001

atto- a 0.000 000 000 000 000 001


Simple Conversion

• conversion from one unit to another is as simple as moving the decimal point– move decimal point to leftleft to convert to larger units– move decimal point to rightright to convert to smaller units

1018 1015 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18

E P T G M k h da 1 d c m μ n p f a


Derived vs Fundamental Units

• Fundamental UnitsFundamental Units– measure or describe basic qualities of any physical

object or phenomena• mass• length• time

• Derived Units– ones formed from new mathematical expressions

needed to quantify qualities of a physical object• area• density• volume• speed• concentration


SI Derived Unit Quantities

Quantity Name Symbol Base Unit

area square meter m2 m2

volume cubic meter m3 m3

speed meter per second m/s m/s

density kilogram per cubic meter kg/m3 kg/m3

concentration mole per cubic meter mol/m3 mol/m3

force newton N m●kg/s2

pressure pascal Pa kg/m●s2

energy joule J m2●kg/s2


Common Non SI unitsQuantity Name Symbol

time minute

hour

day

min

h

d

volume liter

milliliter

L

mL

density gram per milliliter g/mL

temperature degree Celsius oC

distance angstrom pressure millimeter of mercury

atmosphere

mm Hg

atm

energy calorie cal


Uncertainty in Measurement• limited by the accuracy of the tools

being used to make them• some digits are certain and the final

digit is an estimate– 6.25 --- 6.2 is certain the .05 is estimate


Accuracy Versus Precision

• AccuracyAccuracy– quality of the measuring instrument as compared with

the standard for that measurement– how close is the measurement to the actual standard

• PrecisionPrecision– the degree of exactness with which a measurement is

taken– reproducibility of measurements– uncertainty of measurement


Significant Figures• all the digits that

are well known plus one estimated figure represent the significant figures in a measurement

• using a millimeter ruler (6.25) gives more significant digits (3) and greater precision that a centimeter (6.1) ruler with less significant digits (2)


Use of Plus or Minus Notation

• Scientist’s use a ± notation to describe the degree of uncertainty– cm ruler

• 6.1 cm ± .5 cm or 61 mm ± .5 mm

– mm ruler• 6.25 cm ± .05 cm or 62.5 mm ± .05 mm


Calculating and Significant Figures• Multiplication/ Division RuleMultiplication/ Division Rule

– express product or quotient to same number of significant figures as the measurement with the fewest significant figures

• i.e.

cmcm

cm

cm

3.10362.10

30.3

14.3


Calculating and Significant Figures• Addition/ Subtraction RuleAddition/ Subtraction Rule

– round the sum or difference so that it has same number of significant figures as the measurement with the fewest significant figures

• i.e.

cmcm

cm

cm

cm

8.2076.20

12.6

3.9

34.5


Percent Error

• Observed ValueObserved Value– value based on laboratory measurement

• True ValueTrue Value– most probable value based on generally

accepted references

• Absolute ErrorAbsolute Error– difference between observed and true value

• Percent ErrorPercent Error– (absolute error/true value) x 100


Calculating Percent Error

• Boiling point of water– observed value 105.25oC– true value 100.0oC

%25.5

%1000.100

25.5

%1000.100

0.10025.105

errorpercent

xerrorpercent

xerrorpercent


Scientific Notation

• makes working with large or small numbers is easier– all numbers expressed as the product

of a number between 1 and 10 and a whole number power of 10

• (M x 10n)

– i.e.• 2000 cm becomes 2 x 103 cm


Calculations in Scientific Notation

• Multiplication– (1 x 10-2) (3 x 105) (2 x 1012) = ?

• multiply M values– (1 x 3 x 2 = 6)

• add exponents– (-2+5+12 = 15)

• (1 x 10-2) (3 x 105) (2 x 1012) = 6 x 1015

• Division– (6 x 105)(2 x 1012) = ?

• divide M values– (6 2 = 3)

• subtract denominator exponent from numerator exponents– (5-12 = -7)

• (6 x 105) (2 x 1012) = 3 x 10-7

Updated Aug 2006Created by C. Ippolito August 2006 Measurement Objectives: list three requirements...

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