Transcript File - Rogers` Honors Chemistry

Chapter 2 Sec 2.3
Scientific Measurement
Vocabulary
14. accuracy
15. precision
16. percent error
17. significant figures
18. scientific notation
19. directly proportional
20. inversely proportional
2.3 Measurements and Their
Uncertainty



A measurement is a quantity that has both
a number and a unit
Measurements are fundamental to the
experimental sciences. For that reason, it
is important to be able to make
measurements and to decide whether a
measurement is correct.
International System of Measurement (SI)
typically used in the sciences
Accuracy and Precision



Accuracy is the closeness of a measurement to the
correct value of quantity measured
Precision is a measure of how close a set of
measurements are to one another
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 and Precision
Accuracy and Precision
Which target shows:
1.
2.
3.
4.
an accurate but imprecise set of measurements?
a set of measurements that is both precise and accurate?
a precise but inaccurate set of measurements?
a set of measurements that is neither precise nor accurate?
A. Determining Error
1. Error = experimental value – accepted value
*experiment value is measured in lab (what you got during
experiment)
* accepted value is correct value based on references (what you
should have gotten)
2. Percent error = [Value experimental – Valueaccepted] x 100%
Valueaccepted
Significant Figures in Measurement
all known digits + one estimated digit
What is the
measured value?
What is the
measured value?
What is the
measured value?
2.3 Practice Problems – Accuracy and Precision
B. Rules of Significant Figures
1. Every nonzero digit in a measurement is
significant (1-9). Ex: 831 g = 3 sig figs
2. Zeros in the middle of a number are
always significant. Ex: 507 m = 3 sig figs
3. Zeros at the beginning of a number are
NOT significant. Ex: 0.0056 g = 2 sig figs
B. Rules of Significant Figures
4. Zeros at the end of a number are only
significant if they follow a decimal point.
Ex: 35.00 g = 4 sig figs
2400 g = 2 sig figs
Sig Fig Practice #1
How many significant figures in the following?
1.0070 m  5 sig figs
17.10 kg  4 sig figs
100,890 L  5 sig figs
3.29 x 103 s  3 sig figs
These all come
from some
measurements
0.0054 cm  2 sig figs
3,200,000 mL  2 sig figs
5 dogs  unlimited
This is a
counted value
C. Significant Figures in Calculations
1. A calculated answer can only be as precise as
the least precise measurement from which it
was calculated
2. Exact numbers never affect the number of
significant figures in the results of calculations
(unlimited sig figs)
a) counted numbers Ex: 17 beakers
b) exact defined quantities Ex: 60 sec = 1min
Ex: avagadro’s number = 6.02 x 1023
C. Significant Figures in Calculations
3. multiplication and division: answer can have
no more sig figs than least number of sig figs in
the measurements used.
4. addition and subtraction: answer can have
no more decimal places that the least number of
decimal places in the measurements used. (not
sig figs)
Rounding Sig Fig Practice #1
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
240 m/s
236.6666667 m/s
Rounding Practice #2
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.74 g
76.26 g
76.3 g
0.02 cm +2.378 cm
2.398 cm
2.40 cm
710 m -3.4 m
706.6 m
707 m
Sec 2.3 Practice Problems – Significant
Figures
R61 Appendix C (1-7)
Sec 2.3 Practice Problems – Significant Figures
Sec 2.3 Practice Problems – Significant Figures
Scientific Notation

An expression of numbers in the form m x 10n
where m (coefficient) is equal to or greater than 1
and less than 10, and n is the power of 10
(exponent)
D. Rules of Scientific Notation
1. Multiplication – multiply the coefficients
and add the exponents
Ex: (3x104) x (2x102) = (3x2) x 104+2 = 6 x 106
2. Division – divide the coefficients and
subtract the exponent in the denominator
from the exponent in the numerator
Ex: (3.0x105)/(6.0x102) = (3.0/6.0) x 105-2 = 0.5 x 103
= 5.0 x 102
D. Rules of Scientific Notation
3. Addition – exponents must be the same
and then add the coefficients
Ex: (5.4x103) + (8.0x102)
(8.0x102) = (0.80x103)
(5.4x103) + (0.80x103) = (5.4 +0.80) x 103 = 6.2 x 103
4. Subtraction – exponents must be the
same and then subtract the coefficients
Sec 2.3 Practice Problems – Scientific Notation
Chapter 2
Section 3 Using Scientific
Measurements
Direct Proportions
• Two quantities are directly proportional to each
other if dividing one by the other gives a constant
value.
•
yx
• read as “y is proportional to x.”
Chapter 2
Section 3 Using Scientific
Measurements
Direct Proportion
Chapter 2
Section 3 Using Scientific
Measurements
Inverse Proportions
• Two quantities are inversely proportional to each
other if their product is constant.
1
• y 
x
• read as “y is proportional to 1 divided by x.”
Chapter 2
Section 3 Using Scientific
Measurements
Inverse Proportion
Vocabulary
14. accuracy
15. precision
16. percent error
17. significant figures
18. scientific notation
19. directly proportional
20. inversely proportional