Transcript Uncertainty in Data

Chem334
Chapter 3, Unit 2
pg 62
Essential Question
 Infer how uncertainties in measurements affect
how a calculated result is presented
State standard
 11.A.4
Section 3.1
 Measurements & Their Uncertainty
Using and Expressing
Measurements
 Measurement= Is a quantity that has both a number
and a unit
 Ex:


37ml
32oC
Key Concept:
 How do measurements relate to science?
Answer:
 Measurements are fundamental to the sciences. For
that reason, it is important to be able to make
measurements and decide whether a measurement is
correct.
What units do scientists use?
 The international system of measurement (SI)
 AKA-metric system
 Decimal based---no fractions.
Essential Question
 Infer why scientists often express numbers in scientific
notation?
Scientific Notation
 Expresses any number as a number between 1 and 10
(known as a coefficient) multiplied by 10 and raised to
a power (known as an exponent)
 Used to express very large or very small numbers
Scientific Notation
 + exponent=really big number
 - exponent=really small number
Practice Problems
Homework:
 Scientific Notation WS #1
 Due by the end of the class.
Pg 64
Accuracy:
 How close a measured value is to an accepted value.
Precision:
 How close a series of measurements are to one
another.
Accuracy & Precision
Key Concept:
 How do you evaluate Accuracy and precision?
Answer:
 To evaluate the accuracy of a measurement, the
measured value must be compared to the correct
value. To evaluate the precision of a measurement you
must compare the values of two or more repeated
measurements.
Accuracy & Precision
Rules for determining Accuracy
and Precision:
1.
For a measurement to be accurate it must be with in 1
digit (the least significant digit-the estimated digit)
of the actual value for the measurement.
Rules for determining Accuracy
and Precision:
For a measurement to be accurate it must be with in 1
(the least significant digit-the estimated digit) of the
actual value for the measurement.
2. For a measurement to be precise, all the
measurements must be with in 1 digit of each other
(the lease significant digit-the estimated digit)
1.
Rules for determining Accuracy
and Precision:
For a measurement to be accurate it must be with in 1
digit (the least significant digit-the estimated digit)
of the actual value for the measurement.
2. For a measurement to be precise it, all the
measurements must be with in 1 digit (the lease
significant digit-the estimated digit)
3. You must know how to use the equipment being
used.
1.
Rules for determining Accuracy
and Precision:
For a measurement to be accurate it must be with in 1
(the least significant digit-the estimated digit) of the
actual value for the measurement.
2. For a measurement to be precise it, all the
measurements must be with in 1 (the lease
significant digit-the estimated digit)
3. You must know how to use the equipment being
used.
4. The measurement can only have 1 estimated digit—
the last one.
1.
Accuracy & Precision
Homework
 Accuracy and precision WS #1
 Due at end of class
Pg 65
What is error?
 The difference between experimental value and
accepted value.
What is percent error?
 Expresses error as a percentage of the accepted value
*you must calculate error before you can calculate
percent error!!!
Practice Problems
 Calculate error & percent error for students A, B, & C .
Homework:
 Percent Error WS #1
 Due by the end of class
Pg66
When recording a measurement, which
numbers are Significant Figures
 All of the known digits plus one
estimated digit
Key Concept:
 Why must measurements be recorded to the correct
number of significant figures?
Answer:
 Measurements must always be recorded to the correct
number of significant figures because calculated
answers often depend on the number of significant
figures in the in the values used in the calculation.
How many significant figures are
reported in each measurement?
Which is the most precise?
How many significant figures are
reported in each measurement?
5.23cm
Rules for Sig Figs:
1.
Digits from 1-9 are always significant
72.3—has three
2.
Captured zeros – between two other significant
digits are always significant
60.5—has three
Rules for Sig Figs:
3.
4.
5.
Zeros to the right of both the decimal place and
another significant digit are significant
6.20—has three
Place holder zeros are not significant
0.0253 & 4320
(each has three)
Counting numbers = infinite number of
significant digits
6 molecules
60 s=1min
*Trick for checking your answer:
Present =>
Yes decimal point
<=Absent
no decimal point
*from first non-zero digit on are significant
Practice Problems:
Homework:
 Pg 68 Practice problems 1 and 2
 How to do book work:
 First & last name, Date, Hour
 Practice problems 1&2, pg68
 Write out the question, then solve the problems.
 Due by end of class
Pg 68
Key Concept:
 How does the precision of a calculated answer
compare to the precision of the measurement used to
obtain it?
Answer:
 In general, a calculated answer cannot be more precise
that the least precise measurement from which it was
calculated.
Rounding Numbers:
1.
2.
If the digit to the right of the last significant
figure is less than 5, do not change it
2.5322.53
If the digit to the right is greater than 5, round up
to the last significant figure
2.5362.54
Rounding Number Rules:
3.
If the digits to the right are 5 followed by a
nonzero digit, round up
2.53512.54
4.
If the digit to the right is a 5 followed by a
zero or no other number, look at the last
significant figure – if it is odd, round up, if it
is even, round down
2.53502.54
2.52502.52
Practice Problems
Homework:
 Practice Problems 3&4, Pg 69
 How to do book work:
 First & last name, Date, Hour
 Practice problems 3&4, pg69
 Write out the question, then solve the problems.
 Due by end of class
Adding and Subtracting with
Significant Figures
 When adding or subtracting your answer can
only show as many decimal places as the
measurement having the fewest number of
decimal places
*add=# of decimal places
Example:
 When we add 3.76g +14.83g + 2.1g = 20.69
 Round to 20.7
Practice Problems
Multiplying and Dividing with
significant figures
 When multiplying or dividing your answer may
only show as many significant figures as the
multiplied or divided measurement showing the
least number of significant figures
*multiply= # of sig. figs.
Practice Problems
Homework:
 Pages 70 and 71, Practice Problems 5-8
 Due by the end of class.
3.1 Section Assessment:
 Pg72, 9-15
 Writing activity
 5-10 sentences
 Do at the end of your notes.
Quick Lab:
 Pg72
 Lab write-up
3.1 Vocab quiz:
 Tomorrow!!!
pg73
Measuring with SI Units
 The International system of units
 Decimal based.
Key Concept: