umcertainty in measurements

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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



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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



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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



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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

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