Measurement and Science

He has it down to an exact science……

What the heck does that mean?

Science is not about being for sure. Science is about exploring options and always being open to other interpretations.

There is no such thing as an exact science!

There is only one thing for certain in science

Nothing is for certain!

Science cannot exist without quantifiable comparisons:

He is tall--- compared to who or what?

He is 7 ft in height-- quantifiable

Tall, short, fat, skinny, long, short, hot, cold…….

…. These are relative terms and not quantities!

Comparisons are meaningless in science unless compared to a standard value.

And those standard values need to be the same for everyone in order to be widely useful!

Fundamental Units of Measure-directly comparable to a standard

Quantity Symbol Unit SymbolLength l Meter m

Mass m Kilogram kg

Time t Second s

temperature T Kelvin K

ElectricCurrent

I Ampere A

Amt. Ofsubstance

n Mole mol

Luminousintensity

I candela cd

These are the only units used in Mechanics

Fundamental Standards for Units in Mechanics

meter (m) now based on wavelengths of light

kilogram (kg) still a non-reproducible standard- chunk of metal in France

second (s) based upon vibrations of a Cesium atom

all other units in Mechanics are combinations (derived) of these three fundamental values!

Derived Units -derived from fundamental units

Velocity (m/s)- meter/second Acceleration (m/s2)- meter per second

squared Force (N)- Newton Energy (J)- Joule Power (w)- Watt

In making measurements, it is important to have a standard for comparison, and to make those measurements with as much precision as possible.

20 30

Definitely more than 20 and less than 30 units!

23, 24, 25?

Definitely more than 24 and less than 25!

24.2 units, 24.3? Either reading is considered correct.

20 30

To call this measurement 20 units would be poor when it is obviously more!

To call this measurement 30 units would be equally lousy because it is obviously less!

24 or 25 would be a better effort and be considered more accurate, even though they contain estimated values.

There is no such thing as an exact measurement--

All measurements are inherently estimates!

All measurements contain some degree of uncertainty depending upon the device.

An accurate measurement will contain all the known values of the measurement plus one (and only one) estimated value.

Why only one? More than one estimated value becomes wild guesses and have no meaning.

An estimate is not a guess-- it is an attempt to approximate and make a reading more precise.

All known values of a measurement plus one estimate are called significant figures (digits).

Significant Figures/DigitsA method of maintaining accuracy and

precision in measurements and calculations.All known values of a measurement or

calculation PLUS one and only one estimated value.

In measurements, SD are totally determined by the device being used.

In calculations, SD in the answer are determined by a basic rule

In a given value, what is a SD?All non-zero numbers are SD’s:

12.35cm (4) 4.26 m (3)

Zeros between other SD count:

102 s (3) 5.007 (4)

Zeros ending decimals count:

12.30 (4) .3400 (4)

Zeros marked with a bar count:

100 (3) 12,000 (4)

When is 0 not a SD?

When it merely shows where the decimal is:

• ending whole numbers (with no bar)

12,000 m (2) 305,000 m (3)

• starting a pure decimal

.0035 cm (2) 0.000240 km (3)

• part of the magnitude of scientific notation

3.50 X 105 J (3)

In calculations, only measured (or values calculated from measurements) count for SD!

The following would have no SD: the accepted value used in finding

experimental error and deviationstandard/accepted values such as the

acceleration due to gravityconstant, non-measured values, such as

Newton’s Universal Gravitational Constant, Pi (π), etc.

Counted values

125.6 mx 2.7 m

General Rules for Calculating in SD:

Find the area in SD:

8 7 9 22 5 1 2 0

3 3 9. 1 2Estimated Values

You might assume the answer to be 339.1 m2

because it is a tenth times a tenth

In SD, only one estimated value is kept!! Therefore, the correct, precise and accurate answer is: 340 m2

Rule for Calculating in SD

In a calculation done in SD, the answer can never be more precise than the least precise part of the

problem!

Rules for Adding and Subtracting in SD

Your answer will have its last SD in the same decimal place as the least precise part of the problem!

11.2 cm + 8.66 cm + 2.345 cm =

last SD in the tenths column

45.3578 L - 23.26 L =

last SD in the hundredths column

Rules for Multiplying and Dividing in SD

Keep the same number of SD in your answer as the smallest (# SD) part of your problem!

(12.6 cm)(11.22 cm)(5.8 cm) =

[3SD][4SD][2SD] 2 SD in your answer

(55.6g)

(11.34cm)(18.345cm)(3.4cm)=

2 SD in your answer

1)   400     2)    200.0 3)  0.0001 4)  218

5)  320    6)    0.00530 7)    22 568

8) 4755.50 

How many significant figures in the following measurements:

Complete these addition problems.a)6.201 cm + 7.4 cm + 0.68 cm + 12.0 cm = b)1884 kg + 0.94 kg + 1.0 kg + 9.778 kg =c) 16. 156 g + 28.2 g + 0.0058 g + 9.44 g =

Complete these subtraction problems.a)10.8 g – 8.264 g = b)2104.1 m – 463.09 m =c) 16.50 mL – 8.0 mL =

Complete these multiplication problems.a)10.19 m x 0.013 m = b)3.2145 km x 4.23 km = c)(7.50 x 106 m)(2.2 x 10-3 m) =

Complete these division problems.a) 80.23 m 2.4 s  b) 4.301 kg 1.9 cm3

6.6 x 108 m 2.31 x 10-2 s

Accuracy and Precision in Labwork

Bad accuracy, good precision Better accuracy, poor

precision

Bad accuracy and precision Good and good

Accuracy and Precision

A way of indicating the the degree of uncertainty in measurements

AccuracyError

• Refers to how close a measured value comes to the accepted value for a quantity

• Absolute error- actual difference

Ea = |O - A| OObserved in lab (data)

AAccepted answer

• Relative Error- comparative miss

Er = Ea/A •100%

PrecisionDeviation• Refers to how well several measurements

agree with each other- about the same average answer each trial

• Absolute Deviation- difference each trial is from the average answer

Da = |O - M| Mmean (average of data)

• Relative Deviation- percentage

Dr = Da (average)/M 100%

Only 1 value for Dr!

A student performs a lab in which he tries to find the acceleration due to gravity. His data produces the following values: 9.5 m/s2 , 8.9 m/s2, 9.9 m/s2, and 9.1 m/s2. Find his accuracy and his precision if the accepted value is 9.8 m/s2.Ea = |O - A|

= | 9.5 - 9.8 |m/s2 = .3 m/s2

= | 8.9 - 9.8 | m/s2 = .9 m/s2

= | 9.9 - 9.8 | m/s2 = .1 m/s2

= | 9.1 - 9.8 | m/s2 = .7 m/s2

Er = Ea/A x 100

= .3/9.8 x 100 = 3%

= .9/9.8 x 100 = 9%

= .1/9.8 x 100 = 1%

= .7/9.8 x 100 = 7%

M = (9.5 + 8.9 + 9.9 + 9.1) m/s2

4 = 9.4 m/s2

Da = |O - M| = |9.5 - 9.4| = .1 m/s2

Da = |O - M| = |8.9 - 9.4| = .5 m/s2

Da = |O - M| = |9.9 - 9.4| = .5 m/s2

Da = |O - M| = |9.1 - 9.4| = .3 m/s2

Avg. Da =

(.1+.5+.5+.3)m/s2

4= .4 m/s2

Dr = Avg Da X 100

M

= .4 / 9.4 X 100 = 4%

Find the accuracy and precision of the following lab done to find the density of a sample of lead (accepted D = 11.6 g/cm3):

Trial 1: 12.3 g/cm3

Trial 2: 11.0 g/cm3

Trial 3: 10.4 g/cm3

Trial 4: 12.8 g/cm3

Trial 5: 13.1 g/cm3