Measuring and Measuring and Recording DataRecording Data

developed in France in 1795developed in France in 1795a.k.a. “SI”a.k.a. “SI” -- International System of UnitsInternational System of Units

The U.S. was (and still is) reluctant to “go metric.”The U.S. was (and still is) reluctant to “go metric.”

• very costly to changevery costly to change• perception of “Communist” systemperception of “Communist” system

• natural resistance to changenatural resistance to change• American prideAmerican pride

The SI unit of:The SI unit of:• length is the length is the metermeter, m, m

• time is the time is the secondsecond, s, s

• mass is the mass is the kilogramkilogram, kg., kg.

• electric charge is the electric charge is the CoulombCoulomb, C, C

• temperature is the degree temperature is the degree KelvinKelvin, K, K

• an amount of a substance is the an amount of a substance is the molemole, mol, mol

• luminous intensity is the luminous intensity is the candlecandle, cd, cd

• The The secondsecond is defined in terms of is defined in terms ofatomic vibrationsatomic vibrations of Cesium-133 atoms. of Cesium-133 atoms.

• The The metermeter is defined in terms of the is defined in terms of the speed of lightspeed of light..

• The The kilogramkilogram is still defined by is still defined byan an official physical standardofficial physical standard..

““Derived units” are combinationsDerived units” are combinationsof these “fundamental units”of these “fundamental units”

Examples include speed in m/s, area in mExamples include speed in m/s, area in m22,,force in kgforce in kg..m/sm/s22, acceleration in m/s, acceleration in m/s22,,

volume in mvolume in m33, energy in kg, energy in kg..mm22/s/s22

10101818 exaexa E E10101515 petapeta P P10101212 teratera T T 101099 gigagiga G G 101066 megamega M M 101033 kilokilo k k 101022 hectohecto h h 101011 dekadeka da da

10101818 attoatto a a10101515 femtofemto f f10101212 picopico p p 101099 nanonano n n 101066 micromicro 101033 milli milli m m 101022 centicenti c c 101011 decideci d d

Explore the metric systemExplore the metric systemat at link1, , link2, and , and link3..

See definitions of metric units here.See definitions of metric units here.Click here to do conversions.Click here to do conversions.

There is no such thing asThere is no such thing asabsolute certaintyabsolute certainty

of a scientific claim.of a scientific claim.

The validity of a scientific conclusion is always limited by:The validity of a scientific conclusion is always limited by:

• the experimentthe experimentdesign, equipment, etc...design, equipment, etc...

• the experimenterthe experimenterhuman error, interpretation, etc...human error, interpretation, etc...

• our limited knowledgeour limited knowledgeignorance, future discoveries, etc...ignorance, future discoveries, etc...

All measurements have some degree of uncertainty.All measurements have some degree of uncertainty.

PrecisionPrecisionsingle measurementsingle measurement - exactness, definitenessexactness, definiteness

group of measurementsgroup of measurements - agreement, closeness togetheragreement, closeness together

AccuracyAccuracycloseness to the accepted valuecloseness to the accepted value

% error% error == accepted - observedaccepted - observed

acceptedaccepted xx 100%100%

Four student lab groups performed data collection activities in order Four student lab groups performed data collection activities in order to determine the resistance of some unknown resistor (you will do this to determine the resistance of some unknown resistor (you will do this later in the course). Data from 5 trials are displayed below.later in the course). Data from 5 trials are displayed below.

Suppose the accepted value for the resistance is 500 Suppose the accepted value for the resistance is 500 ΩΩ. . Then we would classify each groups’ trials as:Then we would classify each groups’ trials as:

Group 1: neither precise nor accurateGroup 1: neither precise nor accurateGroup 2: precise, but not accurate Group 2: precise, but not accurate Group 3: accurate, but not preciseGroup 3: accurate, but not preciseGroup 4: both precise and accurateGroup 4: both precise and accurate

Example of the differences between precision and Example of the differences between precision and accuracy for a set of measurements:accuracy for a set of measurements:

GroupGroup Trial 1Trial 1 Trial 2Trial 2 Trial 3Trial 3 Trial 4Trial 4 Trial 5Trial 5 avgavg

11 3434 612612 7878 126126 413413 132.6132.6

22 126126 127127 126126 128128 125125 126.4126.4

33 2020 500500 6262 980980 938938 500500

44 502502 501501 503503 498498 499499 500.6500.6

The precision, or decimal place, to which a single The precision, or decimal place, to which a single measurement is recorded is determined by the measurement is recorded is determined by the graduations of the measuring device. graduations of the measuring device.

The rule is simple: You record what you know for certain, The rule is simple: You record what you know for certain, and then estimate one more decimal position.and then estimate one more decimal position.

For example, For example, • if a device is marked by if a device is marked by tenstens, you record to the , you record to the onesones place place• if a device is marked by if a device is marked by hundredthshundredths, you record to , you record to the the thousandthsthousandths• if a measurement is recorded to the if a measurement is recorded to the hundredthshundredths, , the device used must have been marked by the device used must have been marked by tenthstenths, etc…, etc…

Example:

This thermometer is marked every 10 degrees. We know for certain that the temperature measurement is between 40 and 50 degrees, so it is “forty-something”. That “something” is what we estimate, and is the last decimal place recorded. Therefore it would be appropriate to call this reading 42 or 43 degrees, but not 43.5 degrees.

“If marked by tens, you record to the ones.”

Example:

Suppose that a weight measurement taken using an analog scale (not digital) is recorded as 168.4 pounds. This reading implies that the scale used must have been calibrated, or marked, by what increments?

Since the weight is recorded to the tenth of a pound, this means that the value in the tenth’s place must be an estimate. The scale had to have been marked in such a way that the measurement was known to be between 168 and 169 pounds. This implies that there must have been markings for 168 and 169, so the scale was marked by pounds (the one’s place).

“If recorded to the tenths, it was marked by ones.”

1. All non-zero digits are significant.1. All non-zero digits are significant.2. Zeros between other significant digits 2. Zeros between other significant digits

are significant.are significant.3. Leading zeros are not significant. 3. Leading zeros are not significant. 4.4. Final zeros before the decimal are not Final zeros before the decimal are not significant.significant.

Operations with Significant DigitsOperations with Significant Digits

Addition and SubtractionAddition and Subtractionround the sum or differenceround the sum or difference

to the least precise decimal placeto the least precise decimal place

Multiplication and DivisionMultiplication and Divisionround so that the product or quotientround so that the product or quotient

has a total number of significant digitshas a total number of significant digitsequal to the total number of significant equal to the total number of significant

digits of the least precise quantity digits of the least precise quantity

Learn more about significant digitsLearn more about significant digitshere and here.here and here.

Check your understanding here.Check your understanding here.

The “bottom line” is that the precision to which aThe “bottom line” is that the precision to which ameasured or calculated amount is written providesmeasured or calculated amount is written providesvaluable information as to the precision (certainty)valuable information as to the precision (certainty)

of that value and the device used to measure it.of that value and the device used to measure it.