Download chm 115 Matter Measurement and Problem Solving reliability

Matter, Measurement, and
Problem Solving
Reliability of Measurement
Reliability of a Measurement
Scientific measurement is reported so that
every digit is certain except the last one,
which is estimated
Sources of Error
All measurements contain error
 Determinant error

◦ Consistent error- i.e. issues with calibration

Indeterminate error
◦ Cause measurements to fluctuate around true
value
◦ Factors beyond control
 Air currents, static, etc.
◦ Cannot completely eliminate
Significant Figures in Measurements
Significant Figures in Measurements
Rules for Significant Figures
Exact numbers and definitions have infinite significant figures
Practice Identifying Significant Figures
102.400 meters
1,200,000 g
4.3020 x 10-8 m
2.030 x 105 nm
25 students
0.00090 cm
19 cm3
2.05 x 107 g
13 eggs
2.37 x 10-2 m
300,000,000 m/s
100 cm = 1 m
Significant Figures in Calculations

Two rules◦ addition and subtraction
 Place value of significant figures
◦ Multiply and divide
 Quantity of significant figures
Addition and Subtraction Rules
Result carries same number of decimal
places as the quantity with fewest decimal
places
Addition Subtraction Practice
2.5 cm + 0.50 cm + 0.055 cm =
Addition Subtraction Practice
416 g - 210 g =
Addition Subtraction Practice
160 + 88.50
Multiplying and Dividing Rule
Result contains same number of significant
figures as factor with fewest significant
figures
Multiplying and Dividing Practice
0.020 cm x 50 cm x 11.1 cm =
Multiplying and Dividing Practice
0.530 g / 0.1010 mL =
Multiplying and Dividing Practice
2.31 cm x 1.5 cm=
Multiplying and Dividing Practice
1300 x 5.9980 =
Precision vs. Accuracy
Accuracy- how close the measured value is to actual value- how exact it is
Precision- how close results are to one another
Accuracy vs. Precision
Percent Error
Can apply to single measurement
 Expresses how much measurement
deviates from true or accepted value

Percent Error Practice
At a track meet, you time a friend running 100 m
in 11.00 seconds. The officials time her at 10.67
seconds. What is your percentage error?
Error of Multiple Measurements

Precision or reproducibility- calculate
average
Standard Deviation
How much are the measurements off by?
Example of Standard Deviation