Transcript Scientific Notation and Significant Figures

Reliability of Measurements
Chapter 2.3
Objectives
 I can define and compare accuracy and
precision.
 I can calculate percent error to describe the
accuracy of experimental data.
 I can use significant figures and rounding to
reflect the certainty of data.
Accuracy and Precision
Often accuracy and precision confused for one another,
but they are different concepts.
ACCURACY
How close the measured
value is to the accepted
value
Ex: How close to the center of the dart
board?
PRECISION
How close a series of
measurements are to one
another
Ex: How close together are all the darts
you throw together?
If you took another measurement, how
close would it be to the others?
Accuracy and Precision
What are the precision and accuracy levels of the following?
Low Accuracy
High Precision
High Accuracy
High Precision
Low Accuracy
Low Precision
Whose data is most accurate/precise?
Three chemistry students measured the mass and
volume of a piece of zinc to determine it’s density.
The table below shows the data:
John
Sam
Sara
Trial 1
7.17 g/mL
7.65 g/mL
7.04 g/mL
Trial 2
7.14 g/mL
7.65 g/mL
7.55 g/mL
Trial 3
7.13 g/mL
7.64 g/mL
7.26 g/mL
Average
7.15 g/mL
7.65 g/mL
7.28 g/mL
Compare the students data.
Whose data is the most accurate and precise?
Percent Error
A way to evaluate the accuracy of data.
Percent Error=Ratio of the error to the accepted value
│Accepted value – Measured value │
X 100%
Accepted value
Percent Error
If your measurement of a liquid is 123.4 mL
but the actual amount is 125.0 mL, what
is the percent error of the
measurement?
125.0 mL – 123.4 mL
________________________________________
125.0 mL
1.6 mL
=
_______________
125.0 mL
X 100%
=
1.3%
Percent Deviation
A way to evaluate the precision of the data.
Percent Deviation=Ratio of your measurements change from the
average compared to the average value
│Mean value – Measured value │
Mean value
X 100%
Percent Deviation
If one of your measurements of the length
of a string was 22.7 cm and the mean
measurement was 22.9 cm, what is the
percent deviation of the measurement?
22.9 cm – 22.7 cm
________________________________________
22.9 cm
0.2 cm
=
_______________
22.9 cm
X 100%
=
0.9%
Significant Figures
 The number of digits reported in a measurement.
 All the known digits plus one estimated value.
 The number of significant figures possible
depends upon the piece of equipment used to take
the measurement.
Significant Figures
Rules for Significant Figures
1.
2.
3.
4.
5.
Non-zero numbers are always significant.
Zeros between non-zeros are always
significant.
All final zeros to the right of the decimal
place are significant.
Zeros that act as placeholders are NOT
significant.
Counting numbers and defined constants have
an infinite number of significant figures.
Practicing Significant Figures
Determine the number of sig figs in the following numbers.
1)0.02
0.02
1
2)70001
70001
5
3)5600
5600
2
4)4.100
4.100
4
5)3.1416
3.1416 (π)
Infinite
(π)
2.80 x 105
3
6)2.80 x
Red numbers=significant
Black numbers=not significant
5
10
Rules for Rounding
If the digit to the immediate right of
the last sig fig is 5-9, round up.
If not, leave as is.
Significant Figures and
Calculators
When using a calculator, you should do the
calculation using the digits allowed by the
calculator and round off only at the end of
the problem.
Do not round off in the
middle of the problem!
Sig Figs and Addition/Subtraction
+ - + - + - + - + - + - + - +
When you add or subtract, you answer must
have the same number of digits to the right
of the decimal point as the original value
with the fewest digits to the right of the
decimal place.
+ - + - + - + - + - + - + - +
Sig Figs and Multiplication/Division
When you multiply or divide, your
ansere must have the same number
of significant figures as the original
value with the least significant
figures.
Practicing Significant Figures
3.33 m2
25 m
53 mL
26.6 g
6.7 cm3