Measurement

Accuracy vs. Precision

Accuracy vs. Precision

“Accuracy and precision are really the same thing.” This statement is:

A. true

B. false

C. true in some cases

D. I don’t know, why don’t you tell me?!

Accuracy vs. Precision

Accuracy describes how close a measurement is to the actual or accepted value.

Precision describes how close multiple measurements are to each other.

Accuracy vs. Precision

An archer shoots six arrows at a target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is:

A. accurate

B. precise

C. both accurate and precise

D. neither accurate nor precise

Accuracy vs. Precision

The same archer shoots six other arrows at the target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is:

A. accurate

B. precise

C. both accurate and precise

D. neither accurate nor precise

Accuracy vs. Precision

The archer shoots six more other arrows at the target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is:

A. accurate

B. precise

C. both accurate and precise

D. neither accurate nor precise

Accuracy vs. Precision

Six more arrows at the target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is:

A. accurate

B. precise

C. both accurate and precise

D. neither accurate nor precise

Accuracy vs. Precision

A good measurement is both accurate and precise.

In summary,

(climatica.org.uk)

Experimental Errors

Experimental Errors

ALL measurements contain errors!

There are two main types of experimental errors: systematic errors random errors

Experimental Errors

Systematic Errors:

affect the accuracy of a measurement.

can usually be eliminated, but are often difficult to detect

are due to the miscalibration or misuse of a measurement device.

result in a consistently high or low measured value.

Experimental Errors

Random Errors:

affect the precision of a measurement.

may be eliminated by averaging multiple measurements.

are due to the unpredictable fluctuations in the readings of a measurement device.

could cause the measured value to be higher or lower than the true value.

Experimental Errors

A student weighs a sample on an electric balance, but forgets to “zero” the balance first causing it to read 0.2 g without anything on it.

This is an example of a

A. systematic error.

B. random error.

C. neither

(www.alibaba.com)

Experimental Errors

A multimeter is used to measure the voltage across a resistor in a circuit. The reading fluctuates up and down around 1.5 V.

This is an example of a

A. systematic error.

B. random error.

C. neither

(learn.sparkfun.com) (minikits.com.au)

Experimental Errors

A police officer measures the speed of a car three times. The measurements are:

50.1 km/h, 50.4 km/h, and 49.6 km/h

This is an example of a

A. systematic error.

B. random error.

C. neither

(www.dailymail.co.uk)

Experimental Errors

The spring in a Newton scale has been stretched beyond it’s elastic limit. When measuring the mass of a 100 g weight, the scale reads 105 g.

This is an example of a

A. systematic error.

B. random error.

C. neither

(ykonline.yksd.com)

Experimental Errors

Mr. Lam is trying to time how long it takes a ball to fall to the ground. He pushes the “reset” button on the timer instead of the “start” button.

This is an example of a

A. systematic error.

B. random error.

C. neither

(www.weiku.com)

Significant Figures

Significant FiguresDoi Inthanon – the highest spot in Thailand

Significant Figures

Since all measurements contain errors, we can not be certain that all of the digits in a measured value are correct.

For example, a student claims to measure the pencil below to be 6.182 cm.

How many of these digits are definitely correct?

Probably only two of them!

Significant Figures

When reporting measured values, use the rule,

“certain, plus one digit”This means that we report all certain digits and also include one uncertain digit.

For example, we round the previous measurement to 6.18 m

All digits, except the last (rightmost) digit of a significant figure are certain.

certain digits uncertain digit

Significant Figures

We call the “certain, plus one” digits of a measurement,

“significant figures” or

“significant digits.”

Significant Figures

Does the number of significant figures reflect the accuracy of a measurement or the precision?

a) accuracyb) precision

The more significant there are, the more precise the measurement is.

Significant FiguresWhich significant digits are certain in the following measurements and which are uncertain?

Measurement Certain Digit(s)

Uncertain Digit

342 s 3, 4 2

103.5 km/h 1, 0, 3 5

9.824 kg 9, 8, 2 4

17.90 m 1, 7, 9 0

460 km 4 6

0.005 C none 5

Significant Figures

How do we know which digits are significant?

Atlantic Ocean

Memorize the following rules:

1. All non-zero digits are significant.

2. Zeros are significant if:

a) they are between non-zero digits.

b) they are to the right of a decimal AND to the right of non-zero digits.

OR use the Pacific-Atlantic “rule”

Significant Figures

Pacific Ocean Atlantic Ocean“Present” “Absent”

First ask yourself, “is the decimal place present or absent?”

Significant Figures

Pacific Ocean“Present”

If the decimal is PRESENT, start on the Pacific side and move along until you reach the first non-zero digit.

13.020

Significant Figures

Pacific Ocean“Present”

Count ALL digits starting from that point.

13.020

Therefore, there are 5 significant figures.

Significant Figures

Pacific Ocean“Present”

Here’s another example.

0.00310

Atlantic Ocean“Absent”

Therefore, there are 3 significant figures.

Significant Figures

If the decimal is ABSENT, start on the Atlantic side and move along until you reach the first non-zero digit.

1604

Atlantic Ocean“Absent”

Significant Figures

Count ALL digits starting from that point.

Therefore, there are 4 significant figures.

Atlantic Ocean“Absent”

1604

Significant Figures

Here’s another example.

Therefore, there are 3 significant figures.

Atlantic Ocean“Absent”

94200

Pacific Ocean“Present”

Significant Figures

How many significant figures are there in the following measurement?

43.0 m

A. 1

B. 2

C. 3

D. 4

E. 5

Significant Figures

How many significant figures are there in the following measurement?

780 m

A. 1

B. 2

C. 3

D. 4

E. 5

Significant Figures

How many significant figures are there in the following measurement?

0.0078 m

A. 1

B. 2

C. 3

D. 4

E. 5

Significant Figures

How many significant figures are there in the following measurement?

0.900 m

A. 1

B. 2

C. 3

D. 4

E. 5

Significant Figures

How many significant figures are there in the following measurement?

9046 m

A. 1

B. 2

C. 3

D. 4

E. 5

Significant Figures

How many significant figures are there in the following measurement?

1000 m

A. 1

B. 2

C. 3

D. 4

E. 5

A. 1

B. 2

C. 3

D. 4

E. 5

Significant Figures

How many significant figures are there in the following measurement?

1000.0 m

A. 1

B. 2

C. 3

D. 4

E. 5

Significant Figures

How many significant figures are there in the following measurement?

6010 m

Operations with Significant

Figures

Adding and Subtracting

RULE:The answer should have the same number of decimal places as the measurement with the least number of decimal places.

356.680

Example

310.4+ 46.280

1 decimal place3 decimal placesround to 1 decimal place 356.7

certain digit + uncertain digit = uncertain digit

Multiplying and Dividing

RULE:The answer should have the same number of significant figures as the measurement with the least number of significant figures.

14365.312

Example

310.4x 46.280

4 significant figures5 significant figuresround to 4 significant figures14370

Multiplying or dividing can not increase the number of significant figures!