Accuracy Precise November 2014

8/9/2019 Accuracy Precise November 2014

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Murphy's Lawsof Science andTechnology:Technology is

dominated by thosewho manage what

they do not

understand.


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Accuracy

Accuracy: How close a measurement/dimension isto the true/actual values

To be accurate requires true value (center eye) andone measurement (one arrow to hit the target).


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Precision

Precision refers to thereproducibilityof a measurement.

Requires several

measurements

(notice multiple arrowholes)

Has nothing to do with the

true value(none of the values are

close to the target but all

the holes are close

together).


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Does this picture representaccuracy or precision

!. Accuracy

". #recision

$. %oth


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Does this picture representaccuracy or precision

!. Accuracy

". #recision

$. %oth


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Accurate and #recise

&n order to be accurate and precise'one must pay close attention to detailto receive the same results every

time as well as hit the target.

A l i h $ !*" + i h d h


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A sample weighs $.!*"gm. +ou weighed thesample , di-erent times getting the above

data $."g' $.!*g' $.!,"g' $.!"0g' 1

$.!*2g. 3hich measurement is the mostaccurateAns: 4ost accurate measurementwould be $.!* g' because it is closest to

the actual weight of the sample.

!. $."g". $.!*g

$. $.!,"g

5. $.!"0g,. $.!*2g


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6onsider the data (in cm) obtained for thelength of an ob7ect as measured by three

students. The length is 8nown to be !5., cm.3hich student had the most precisewor8

!. 9tudent A

". 9tudent %

$. 9tudent 6


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6onsider the data (in cm) obtained for thelength of an ob7ect as measured by three

students. The length is 8nown to be !5., cm.

3hich student had the most accuratewor8

!. 9tudent A

". 9tudent %

$. 9tudent 6


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#roblem :" Answer

Answer: Student Ahad the most precisewor8

since there is only .! cm between the highest

and lowest values' and Student Chad the most

accuratewor8 since two of the measurementswere e;actly at the true value and the other three

measurements were within .! cm of the actual

value.


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In order to win the archery tournament, the archer must hit the target the most

times.

The winner must be accurate and precise.

The first archer is just precise. He or she hit the same area of the target every

time

The second archer was accurate because he hit the target once.

However, the third archer was accurate and precise because he or she hit the

target every time. Therefore, he or she wins!

Poor accuracy

Good precision

Good accuracy

Poor precision

Good accuracy

Good precision


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#ercent


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raduated 6ylinder B4eniscus


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Data Cuality

Accuracy recision " #ua$ity

%rror " fn&accuracy, precision'

(ost vs. )ua$ity tradeoff


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andom and 9ystematic

error*ystematic errors affect accuracy, but areusua$$y independent of precision+ data can use

high$y precise methods but sti$$ be inaccurate due

to systematic errorAccurate andprecise no

systematic, $itt$e

random error

inaccurate andprecise $itt$e

random error but

significant

systematic error

Accurate and

imprecise no

systematic, but

considerab$e random

error

inaccurate andimprecise both

types of error


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4easurement of Accuracy

ositiona$ accuracy is often stated as a

confidence interva$ e.g. -/.0 cm 12 .-

means true va$ue $ies between -/.0- and-/.-3

-/.-3 -/.0 -/.0- -/.00-/.-4


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4easurement of Accuracy5ne of the 6ey measurements of positiona$

accuracy is root mean s)uared error &7*%'+

e)ua$s s)uared difference between observed

and e8pected va$ue for observation idivided bytota$ number of observations, summed across

each observation i

This is just a standardi9ed measure of error:how

c$ose the predicted measure is to observed


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Accuracy How close the experimentallymeasuredvalue is to the acceptedvalue

#recision How close is the experimentallymeasuredvalue to the otherexperimentally measuredvalues


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4att Eohn Dan #ete

Assuming the center bullFsBeye is our accepted value3ho is the most accurate at throwing darts3ho is the least precise

Describe EohnGs precision and accuracy to the other dart throwers.


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recision and Accuracy

;ow recision High recision

;ow

Accuracy

High

Accuracy


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Sources of Error

2 *amp$e errors

2


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Sources of Error

Sample Errors

2 *amp$e container contaminated.

2 Incorrect samp$e $ocation.

2 Non2representative samp$e.

2 Incorrect samp$e container.

2 *amp$e mi8 up.


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Sources of Error

Reagent Errors

2 Impure reagents or so$vents.

2 Improper storage of reagents.

2 Neg$ect of reagent e8piration date.

2 %vaporated reagents.

2 (onsideration of different purities or grades.


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Sources of Error

Reference Material Errors

2 Impurity of reference materia$s.

2 %rrors from interfering substances.

2 (hanges due to improper storage.2 %rrors in preparing reference materia$.

2 =sing e8pired reference materia$.


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Sources of Error

General Method Errors

2 >eviating from the ana$ysis procedure.

2 >isregard for the $imit of detection.

2 >isregard for a b$an6 correction.2 (a$cu$ation errors &di$utions, mi8tures,

additions'.

2 Not using the correct ana$ytica$ procedure.


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Sources of Error

Calibration Errors

2 ?o$umetric measuring errors.

2 @eighing errors.2 Inaccurate e)uipment adjustments.


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Sources of Error

Equipment Errors

2 %)uipment not c$eaned

2 7aintenance neg$ected.2 Temperature, e$ectrica$, and magnetic effects.

2 %rrors in using pipettes &not ca$ibrated, pipette tip not

correct$y attached, contamination'.

2 %rrors in using g$ass pipettes &damaged, badtechni)ue, contamination'.


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Sources of Error

Equipment Errors (continued) (uvette errors &defects not considered, unsuitab$e

cuvette g$ass, not fi$$ed to minimum, wet on the

outside, air bubb$es, contamination'. hotometer errors &wrong wave$ength, insufficient

$amp intensity, dirty optics, drift effect ignored,

incorrect$y set 9ero, $ight entering the samp$e

chamber'.


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Sources of Error

*igna$


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Sources of Error

(a$cu$ation %rrors

2 Arithmetic errors, decima$ point errors, incorrect

units.

2


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Sources of Error

%rrors in


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Accuracy and #recision

4uch of science has to do withcollection and management ofquantitative or numerical data.

The value of computations usingnumerical data is greatly dependenton the accuracy and precision of that

data.


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There is always some degree of


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Accuracy and precision can not beconsidered independently

A number can be accurate and not

precise A number can be precise and not

accurate

The use of the number determines therelative need for accuracy andprecision


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A66IA6+

Accuracy can be deJned as howclose a number is to what it shouldbe.

Accuracy is determined bycomparing a number to a 8nown oraccepted value.


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#


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Accuracy vs. #recision for


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Accuracy vs. #recision for


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Accuracy vs. Precision forExample 3

4ary is reasonably accurate. 9hewas not very precise because thebalance was capable of measuring to

two decimal places. Ashley is much more accurate

because of the precision of her

measurement andcloseness of hervalue to the actual value.


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A66IA6+/#


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&n 6onclusion

&n science we depend upon both theaccuracy and precision of thenumbers we use.

The need for accuracy and precisionvaries with the circumstance andother measurements being used.


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4easurements

Mength meters

Nolume (space occupied by anob7ect) meter$ > B liter

4ass (measured by comparing massof ob7ect to standard mass of !8g)gram

Density (ratio of mass of an ob7ect toits volume dm!v) g/m$>orB g/l

Temperature O6 or P


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ACCRAC!ACCRAC!


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ercent error is used to estimate the accuracy of a measurement.ercent error is used to estimate the accuracy of a measurement.

ercent error wi$$ a$ways be a positive.ercent error wi$$ a$ways be a positive.

@hat is the percent error if the measured density of titanium &Ti' is /./D g1cm@hat is the percent error if the measured density of titanium &Ti' is /./D g1cmCCand theand the

accepted density of Ti is /.D g1cmaccepted density of Ti is /.D g1cmCCEE

PREC.S.%/PREC.S.%/


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Average " -D.C Fg1;Average " -D.C Fg1;

*tandard >eviation " 0.- Fg1;*tandard >eviation " 0.- Fg1;

@hat is the true concentration of As in this e8perimentE@hat is the true concentration of As in this e8perimentE

%stimate the accuracy of this method.%stimate the accuracy of this method.

How precise is this methodEHow precise is this methodE

Precision is the agreement bet*een repeated measurements of thePrecision is the agreement bet*een repeated measurements of the

same sample+ Precision is usually e,pressed as a standard de-iation+same sample+ Precision is usually e,pressed as a standard de-iation+ Bor e8amp$e, the precision of a method for measuring arsenic &As' wasBor e8amp$e, the precision of a method for measuring arsenic &As' was

determined by measuring G different so$utions each containing -/.C Fg1; ofdetermined by measuring G different so$utions each containing -/.C Fg1; of

As.As.

MeasuredMeasuredConcentrationConcentration

(0g1)(0g1)-4./-4./

-C.-C.

-C.-C.

-/.0-/.0

-.-.

-C.-C.

-G.4-G.4

-/.C Fg1;-/.C Fg1;

0.- Fg1;0.- Fg1;

ACCRAC! A/" PREC.S.%/ACCRAC! A/" PREC.S.%/


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>escribe the accuracy and precision of these / targets.>escribe the accuracy and precision of these / targets.

Accurate, andAccurate, and

precisepreciserecise, butrecise, but

not accuratenot accurateAccurate, butAccurate, but

not precisenot preciseNot accurate,Not accurate,

and notand not

preciseprecise

ERR%RSERR%RS


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Systematic (or determinate) errors are reproducible and cause a bias in theSystematic (or determinate) errors are reproducible and cause a bias in the

same direction for each measurement+same direction for each measurement+

Bor e8amp$e, a poor$y trained operator that consistent$y ma6es the same mista6e wi$$Bor e8amp$e, a poor$y trained operator that consistent$y ma6es the same mista6e wi$$cause systematic error. *ystematic error can be corrected.cause systematic error. *ystematic error can be corrected.

Random (or indeterminate) errors are caused by the natural uncertainty thatRandom (or indeterminate) errors are caused by the natural uncertainty that

occurs *ith any measurement+occurs *ith any measurement+


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y convention, a measurement is recorded by writing a$$ e8act$y 6nown numbers andy convention, a measurement is recorded by writing a$$ e8act$y 6nown numbers and

- number which is uncertain, together with a unit $abe$.- number which is uncertain, together with a unit $abe$. A$$ numbers written in this way, inc$uding the uncertain digit, are ca$$ed significantA$$ numbers written in this way, inc$uding the uncertain digit, are ca$$ed significant

figures.figures.

Bor e8amp$e, the b$ue $ine is 0.GC cm $ong. This measurement has C significantBor e8amp$e, the b$ue $ine is 0.GC cm $ong. This measurement has C significant

figures. The first 0 digits &0.G cm' are e8act$y 6nown. The third digit &.C cm' isfigures. The first 0 digits &0.G cm' are e8act$y 6nown. The third digit &.C cm' is

uncertain because it was interpo$ated or estimated - digit beyond the sma$$estuncertain because it was interpo$ated or estimated - digit beyond the sma$$est

graduation.graduation.

./2ERP%1A2.%/ A/" S.G/.3.CA/2 3.GRES./2ERP%1A2.%/ A/" S.G/.3.CA/2 3.GRES


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@hat is the vo$ume of water in this graduated cy$inderE A$ways measure the vo$ume@hat is the vo$ume of water in this graduated cy$inderE A$ways measure the vo$ume

of a $i)uid at the bottom of the meniscus. The units are m;.of a $i)uid at the bottom of the meniscus. The units are m;.

The vo$ume of water is D0.4 m;. The D0 m; are e8act$y 6nown, and the .4 m; isThe vo$ume of water is D0.4 m;. The D0 m; are e8act$y 6nown, and the .4 m; is

uncertain because it was interpo$ated or estimated - digit beyond the sma$$estuncertain because it was interpo$ated or estimated - digit beyond the sma$$est

graduation.graduation.

S.G/.3.CA/2 3.GRES A/" 4ER%SS.G/.3.CA/2 3.GRES A/" 4ER%S


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Jeros between non9ero digits are significant. That is, D4 cm has C significantJeros between non9ero digits are significant. That is, D4 cm has C significant

figures.figures. ;eading 9eroes mere$y $ocate the decima$ point and are never significant. That is,;eading 9eroes mere$y $ocate the decima$ point and are never significant. That is,

./3G cm e)ua$s /.3G 8 -./3G cm e)ua$s /.3G 8 -2020cm and has C significant figures.cm and has C significant figures. Trai$ing 9eros are significant as fo$$ows D. m; has C significant figures, D. m; hasTrai$ing 9eros are significant as fo$$ows D. m; has C significant figures, D. m; has

0 significant figures, and D m; has - significant figure.0 significant figures, and D m; has - significant figure.

>atum>atum&grams'&grams'

Number ofNumber of*ignificant*ignificant

BiguresBigures

>atum>atum&mi$$i$iters'&mi$$i$iters'

Number ofNumber of*ignificant*ignificant

BiguresBigures

-,C/-,C/-.34-.34

.C0.C0././-D-D

.-.-

-D.-D..GD.GD

.D/.D/D.4 8 -D.4 8 -2G2G

C/C/

.GC.GC

DD

//

00

00

00

CC

CC

CC

00

CC

CC

CC

S.G/.3.CA/2 3.GRES5 A"".2.%/5 A/" S62RAC2.%/S.G/.3.CA/2 3.G

RES5 A"".2.%/5 A/" S62RAC2.%/


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@hen adding or subtracting do N5T e8tend the resu$t beyond the first co$umn with a@hen adding or subtracting do N5T e8tend the resu$t beyond the first co$umn with a

doubtfu$ figure. Bor e8amp$e, Kdoubtfu$ figure. Bor e8amp$e, K

S.G/.3.CA/2 3.GRES5 A"".2.%/5 A/" S62RAC2.%/S.G/.3.CA/2 3.G

RES5 A"".2.%/5 A/" S62RAC2.%/


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@hat is -.4G/ 0.E@hat is -.4G/ 0.E

@hat is -.4G/ 2 0.E@hat is -.4G/ 2 0.E

S.G/.3.CA/2 3.GRES5 M12.P1.CA2.%/5 A/" ".7.S.%/S.G/.3.CA/2 3.GRES

5 M12.P1.CA2.%/5 A/" ".7.S.%/


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@hen mu$tip$ying or dividing the answer wi$$ have the same number of significant@hen mu$tip$ying or dividing the answer wi$$ have the same number of significant

digits as the $east accurate number used to get the answer. Bor e8amp$e, Kdigits as the $east accurate number used to get the answer. Bor e8amp$e, K

0.D g 1 /.3D m; " ./D g1m;0.D g 1 /.3D m; " ./D g1m;

@hat is -.4G/ 8 0.E@hat is -.4G/ 8 0.E

@hat is -.4G/ 1 0.E@hat is -.4G/ 1 0.E

S.G/.3.CA/2 3.GRES A/" CA1C1A2.%/S 2#A2 RE8.RE M12.P1E S2EPSS.G/.3.CA/2 3.GRES A/" CA1C1A2.%/S 2#A2 RE8.RE M12.P1E S2EPS


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AnAn a-eragea-erageis the best estimate of the true va$ue of a parameter.is the best estimate of the true va$ue of a parameter. AA standard de-iationstandard de-iationis a measure of precision.is a measure of precision.

Averages and standard deviations re)uire severa$ steps to ca$cu$ate. Lou must 6eepAverages and standard deviations re)uire severa$ steps to ca$cu$ate. Lou must 6eep

trac6 of the number of significant figures during each step. >otrac6 of the number of significant figures during each step. >o /%2/%2discard or rounddiscard or round

any figures unti$ the fina$ number is reported.any figures unti$ the fina$ number is reported.

S.G/.3.CA/2 3.GRES A/" CA1C1A2.%/S 2#A2 RE8.RE M12.P1E S2EPSS.G/.3.CA/2 3.GRES A/" CA1C1A2.%/S 2#A2 RE8.RE M12.P1E S2EPS


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$ Significant

3igures

9 Significant 3igure

$ Significant 3igures

& Significant 3igures



Significant 3igures:

@hat is average and standard deviation for the fo$$owing C measurements of the@hat is average and standard deviation for the fo$$owing C measurements of the

same samp$eEsame samp$eE


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same samp$eEsame samp$eE


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05

Accuracy

'ow close a measurement is to the actual ortrue value

good accuracy

true value

poor accuracy

true value


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0,

Precision

'ow well several measurementsagree with each other

good precision

poor precision


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00

Accuracy and Precision

(hat can you say about the accuracyand precision in each of the following:

)ood precision* poor accuracy

)ood precision* good accuracy


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0Q

+n your new ,ob* you are to ma-e thepias the sie shown above. /our

0rst four pias are shown below.

(hat can you say about the accuracyand precision of your pias1


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0*

(hat can you say about theaccuracy and precision of the nextfour pias1

2he next four pias.


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02

Accuracy is improving.

2he two pias in the centershow good accuracy. 'owever*the precision is poor.


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Accuracy and PrecisionAt the conclusion of our

time together* you shouldbe able to:

-. %8p$ain the difference between the accuracyand precision

0. Mive e8amp$es of accuracy and precision


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Accuracy

Accuracy = the e;tent to which ameasured value agrees with a standardvalue

Accuracy of a device must be chec8ed

Does it read a proper acceptedvalue

%eware of Parallax> the apparent shift in

position when viewed at a di-erent angle.

)raduated Cylinder


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)raduated Cylinder 4eniscus and Parallax


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Precision

#recision = the degree of e;actnessof a measurement that is repeatedlyrecorded.

3hich set is more precise!*." ' !*.5 ' !*.$,

!Q.2 ' !*.$ ' !*.*,

!0.* ' !Q." ' !2.55


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Example: Precision

3ho is more precise when measuring thesame !Q. cm boo8

9usan

!Q. cm' !0. cm' !*. cm' !,. cm

Amy

!,., cm' !,. cm' !,." cm' !,.$ cm


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Accuracy vs. Precision

HighAccuracy

High#recisionHigh#recision

MowAccuracy


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(hy +s 2here 5ncertainty


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(hy +s 2here 5ncertainty

7easurements are performed with instruments,and no instrument can read to an infinite number of

decima$ p$aces

Which of the instruments belowhas the greatestuncertainty in measurementE


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Accuracy and Precision6et7s see if you can:

-. %8p$ain the difference between the accuracyand precision

0. Mive e8amp$es of accuracy and precision


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following are precise' accurate orboth.

Low Accuracy

Low Precision

Low Accuracy

High Precision

High

Accuracy

High


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Signi0cant 8iguresAt the conclusion of our time

together* you should be ableto:

-. %8p$ain what significant figures are in a

measurement

0. >etermine the number of significant figures

in any measurement

9i iJ i


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9igniJcant Ligures

The signiJcant Jgures in a measurement

include all of the digits that are 8nown'plus one last digit that is estimated.The numbers reported in a measurement are

limited by the measuring tool.

4easurement and


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4easurement andSigni0cant 8igures


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To indicate the precision of ameasurement' the value recorded should

use all the digits 8nown with certainty'plus one additional estimated digit thatusually is considered uncertain by plusor minus !.

Kofurther insigniJcant digits should berecorded.

The total number of digits used toe;press such a measurement is called

the number of signiJcant Jgures. All but one of the signiJcant Jgures are

8nown with certainty. The last signiJcantJgure is only the best possible estimate.

6elo* are t*o measurements of the


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mass of the same ob;ect+ 2he same

quantity is being described at t*o

different le-els of precision orcertainty+

Accuracy Precise November 2014

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Transcript of Accuracy Precise November 2014