Download - Umcertainty in Measurements
7/27/2019 Umcertainty in Measurements
http://slidepdf.com/reader/full/umcertainty-in-measurements 1/4
8/25/200
U n c e r t a i n t y nn c e r t a i n t y nM e a s u r em e n te a s u r em e n t
Metric Measure, Significant FiguresMetric Measure, Significant Figures& Dimensional Analysis& Dimensional Analysis
Me t r i c f ac t se t r i c f a c t s
First developed in France in the late 18First developed in France in the late 18thth
centurycentury
Used b most countries throu hout theUsed b most countries throu hout theworldworld
Based on the decimal systemBased on the decimal system
Divide or multiply units by 10Divide or multiply units by 10
S I Un i t sI U n i t s
Seven base unitsSeven base units
Uses prefixes to indicate decimal fractionUses prefixes to indicate decimal fractionor multi les of various unitsor multi les of various units
Ex.Ex. millimilli-- 1010--33 fraction of a unitfraction of a unit
millimilligram (gram (mmg) is 10g) is 10--33 gram (g)gram (g)
Prefix
S I B a s e Un i t sI B a s e U n i t sPhysicalQuantity
Name of Unit Abbreviation
Mass Kilogram kg
Length Meter (re) m
Volume Liter (re) l
Time Second s
Electric current Ampere A
Temperature Kelvin K
Luminous intensity Candela cd
Amount of
substance
Mole mol
S e l e c t e d Pr e f i x e se l e c t e d P re f i x e s
U s e d n t h e S I S y s t ems e d n t h e SI S y s t em
PrefixPref ix Abbr. Abbr. MeaningMeaning ExampleExample
Mega- M 106 1 megameter(Mm) = 1x106 m
- =
Deci- d 10-1 1 decimeter (dm) = 0.1 m
Centi- c 10-2 1 centimeter (cm) = 0.01 m
Milli- m 10-3 1 millimeter (mm) = 0.001 m
P re c i s i o n a n d A c c u r a c yr e c i s io n a n d A c c u r a c y Two kinds of numbers Two kinds of numbers
ExactExact
Those whose values are known exactly Those whose values are known exactly 12 eggs in a dozen12 eggs in a dozen
1000 g in a kilogram1000 g in a kilogram . cm n an nc. cm n an nc
InexactInexact
Those obtained by measurements Those obtained by measurements Equipment errorsEquipment errors
Human errorsHuman errors
Remember: Uncertainties always exist inRemember: Uncertainties always exist inmeasured quantitiesmeasured quantities
7/27/2019 Umcertainty in Measurements
http://slidepdf.com/reader/full/umcertainty-in-measurements 2/4
8/25/200
PrecisionPrecision Measure of how closely individualMeasure of how closely individual
measurement agree with one anothermeasurement agree with one another
ccuracyccuracy Refers to how closely individualRefers to how closely individual
measurements agree with the correct, ormeasurements agree with the correct, or“true” value“true” value
The more precise the measurement, the The more precise the measurement, themore accurate it will be.more accurate it will be.
Bu l l ’ s E y eu l l ’ s Eye
Poor accuracy
Good precision
Good accuracy
Good precision
Poor accuracy
Poor precision
S ig n i f i c a n t F ig u r e si g n i f ic a n t F ig u r e s All nonzero digits are significantAll nonzero digits are significant
457 cm (three significant figures)457 cm (three significant figures)
2.5 g (two significant figures)2.5 g (two significant figures)
ZerosZeros betweenbetween nonzero digits are significantnonzero digits are significant
1.03 cm (three significant figures)1.03 cm (three significant figures)
Zeros to theZeros to the leftleft of the first nonzero digit areof the first nonzero digit are notnot
significant (they indicate the position of thesignificant (they indicate the position of thedecimal pointdecimal point
0.02 g (one significant figure)0.02 g (one significant figure)
0.0026 cm (two significant figure)0.0026 cm (two significant figure)
Zeros that fall both at theZeros that fall both at the endend of aof anumber and to the right of the decimalnumber and to the right of the decimalpointpointareare significantsignificant
0.0200 g (three significant figures)0.0200 g (three significant figures)
3.0 cm (two significant figures)3.0 cm (two significant figures)
Numbers ending in zeros but contains noNumbers ending in zeros but contains nodecimal point, the zeros may or may notdecimal point, the zeros may or may notbe significantbe significant
10,300 g (three, four or five significant figures)10,300 g (three, four or five significant figures)
1.03 x 101.03 x 1044 g (three significant figures)g (three significant figures)
1.030 x 101.030 x 1044 g (four significant figures)g (four significant figures)
1.0300 x 101.0300 x 1044 g (five significant figures)g (five significant figures)
N ow e t ’s t r y…ow e t ’s t r y…
How many significant figures are in eachHow many significant figures are in eachof the following numbersof the following numbers
4.0034.0032323..
50005000
3.549 g3.549 g
2.3 x 102.3 x 1044 cmcm
0.00134 m0.00134 m33
7/27/2019 Umcertainty in Measurements
http://slidepdf.com/reader/full/umcertainty-in-measurements 3/4
8/25/200
S ig n i f i c a n t F ig u r e s ni g n i f ic a n t F ig u r e s n
Ca l c u l a t i o n sa l c u l a t i o n s
Multiplication and DivisionMultiplication and Division
Answer follows the number of significant figures inAnswer follows the number of significant figures inthethenumber with the fewest significant figures.number with the fewest significant figures.
correct number of significant figures.correct number of significant figures.
Area = (6.21 cm)( Area = (6.21 cm)( 5.25.2 cm) =cm) = 3232.3492 cm.3492 cm22
Round off to 32 cm2
Addition and SubtractionAddition and Subtraction Result should follow the same number of Result should follow the same number of
decimal places as that of the term with thedecimal places as that of the term with the..
20.4
1.322
83
104.722
One decimal place
Three decimal places
Zero decimal places
Round off to 105
This number limits
the number of
significant figures in
the result
D im e n s i o n a li m e n s i o n a l
A n a l y s i sn a l y s i s
Co n v e rs i o n f a c t o ro n v e r s io n f a c t o r
A fraction whose numerator andA fraction whose numerator anddenominator are the same quantitydenominator are the same quantityexpressed in different unitsexpressed in different units
. . .. . .
2.54 cm. =1 in.2.54 cm. =1 in.
Two conversion factors Two conversion factors
2.54 cm.2.54 cm. 1 in.1 in.
1 in.1 in. 2.54 cm.2.54 cm.
Co n v e r t 8 .5 0 n . t o cm .o n v e r t 8 .5 0 n . t o c m .
Desired unit
(8.50 in.). cm.
1 in.
= 21.6 cmNo. of cm. =
Given unit
No t e t h i s !o t e t h i s !
Given unit X
Desired unit
= Desired unitGiven unit
7/27/2019 Umcertainty in Measurements
http://slidepdf.com/reader/full/umcertainty-in-measurements 4/4
8/25/200
T h e r e f o r e :h e r e f o r e :
What data are you given in the problem?What data are you given in the problem?
What quantity do you wish to obtain inWhat quantity do you wish to obtain inthe roblem?the roblem?
What conversion factors do you haveWhat conversion factors do you haveavailable to take you from the givenavailable to take you from the givenquantity to the desired one?quantity to the desired one?
Now e t ’ s t r y t h i s :o w e t ’ s t r y t h i s :
A man weighs 185 lb. What is his massA man weighs 185 lb. What is his massin grams?in grams?
Conversion factor =1 lb =453.6 gConversion factor =1 lb =453.6 g
Determine the length in kilometers of aDetermine the length in kilometers of a500.0500.0--mi automobile racemi automobile race
Conversion factor =use your table of Conversion factor =use your table of conversion factorsconversion factors
Co n v e r t 1 8 5 b s t o g r am so n v e r t 1 8 5 b s t o g r am s
Desired unit
(185 lb.). .
1 lb.
= 83916 gNo. of g. =
Given unit
Co n v e r t 5 0 0 . 0 m i l e s t o k mo n v e r t 5 0 0 .0 m i le s t o k m
Desired unit
Sig figs… 804.67km =Sig figs… 804.67km = 805km805km Remember, fewest amount of sf in problem are
reflected in answer
500.0 miles.
1 mile
= 804.67 kmNo. of km=
Given unit