Transcript lhhslibertyhill.sharpschool.com

Using and Expressing Measurements
Learning Objectives
 Write numbers in scientific notation.
 Evaluate accuracy and precision.
 Explain why measurements must be reported to the
correct number of significant figures.
Two types of data that is gathered:
Qualitative: descriptive data
Quantitative: numerical data
Scientific Notation
Scientific notation is used to express very large and very small
numbers.
Width of human hair = 0.00007 m
= (7 × 0.00001) m
= 7 × 10–5 m
Writing Numbers in Scientific Notation
Scientific notation includes a coefficient and an exponent.
6,300,000 = 6.3 × 106
Coefficient: number
between 1 and 10
Exponent: power of 10
0.0000074 = 7.4 × 10–6
In class practice: Write each of these
numbers in scientific notation:
17
3
500.0
215
7,000,631
1.7 x 101
3x
100
5.000 x 102
2.15 x
102
7.000631 x 106
0.000000614
6.14 x 10-7
0.0037004
3.7004 x 10-3
0.00000038
0.01010
0.00000000001
3.8 x 10-7
1.010 x 10-2
1 x 10-11
Accuracy and Precision
Accuracy and precision relate to the reliability of a measurement.
Accuracy refers to how close experimental measurements are to the actual
(book) value.
Precision refers to how closely the data gathered is to each other.
Good accuracy
Poor accuracy
Poor accuracy
Good precision
Good precision
Poor precision
YOU TRY IT. THREE STUDENTS PERFORMED AN
EXPERIMENT SEVERAL TIMES AND OBTAINED THE
FOLLOWING RESULTS. THE ACTUAL VALUE OF THE
MASS WAS 9.00 G. WHICH OF THESE DATA SETS (IF
ANY) SHOW BETTER RESULTS?
Student 3 has the best results
Student 1
Student 2
Student 3
9.28 g
9.27 g
9.50 g
9.48 g
9.00 g
9.01 g
9.05 g
9.10 g
9.52 g
9.50 g
8.98 g
9.00 g
9.30 g
9.25 g
9.49 g
9.51 g
9.03 g
9.04 g
Low accuracy
Low precision
Low accuracy
High precision
High accuracy
High precision
Error and Percent Error
Error is a description of how far a measurement is from its
accepted value.
Calculating Percent Error
The boiling point of pure water is measured to be 99.1°C.
Calculate the percent error.
Calculating Percent Error, cont.
The boiling point of pure water is measured to be 99.1°C.
Calculate the percent error.
Significant Figures
Significant figures indicate the precision of a measurement.
Rules for Determining Significant Figures
1. Every nonzero digit in a reported measurement is assumed
to be significant and Zeros appearing between nonzero digits
are significant.
2. Leftmost zeros appearing in front of nonzero digits are not
significant. (Leading zeros are not significant.)
3. Zeros at the end of a number and to the right of a decimal
point are always significant.
4. For values written in scientific notation, the digits in the
coefficient are significant.
5. Counted numbers and exact conversion factors have an
infinite number of significant figures.
The rules are given to you on your reference material.
We will learn how to apply and use those rules.
ALWAYS refer to the rules.
1. Non-zero digits and zeros between non-zero digits
are always significant.
Number
Number of Significant
Figures
125
3
1142
4
2005
4
7
1000007
2. Leading zeros are not significant.
Leading zeros are zeros that precede all
nonzero digits. These zeros do not
count as significant figures.
0.0025
2 sig
figs
0.0321
3 sig
figs
3. Zeros to the right of all non-zero digits are
only significant if a decimal point is shown.
These are called trailing zeros.
Examples:
100
1 sig fig
100.
3 sig fig
4. For values written in scientific
notation, the digits in the coefficient are
significant.
Examples:
1.00×102
2.0560 x
104
3 sig fig
5 sig fig
5. In a common logarithm, there are as
many digits after the decimal point as
there are significant figures in the
original number. (log base 10)
Examples:
Log 75 is 1.87 which is two sig figs.
WHOA!! Ok how? Let’s look at it this way:
74 is 7.4x101
Now consider the log of each
part: the log of 101 is 1, an exact
number
The log of 7.4 is 0.87 -- with a proper 2 SF.
Add those together, and
you get log 74 = 1.87 -with 2 SF.
Pacific
Ocean
Decimal
Present:
Start on the
left of the
number and
don’t start
counting sig
figs until you
get to the
first non-zero
number.
Memory
Helper
Atlantic
Ocean
Decimal
Absent.
Start on the
right side of
the number
and don’t
start
counting sig
figs until
you get to
the first
non-zero
Number of
Sig Figs
Number of
Sig Figs
0.02
1
142
3
0.020
2
0.073
2
501
3
1.071
4
501.0
4
10810
4
5.00
3
5000
1
Round each of the following to three significant
digits.
Rounded
Number
88.473
8505
976450
699.5
123.98
0.00086321
88.5
8510
976000
700.
124
0.000863
Rounded
Number
69.95
70.0
0.000056794
0.0000568
67.048
67.0
3.002
3.00
0.0300
0.0300
90100
90100