Transcript Chem 160- Ch # 2l. - Solano Community College

Chem 160- Ch # 2l.
Numbers from measurements.
Measurements
• Experiments are performed.
• Numerical values or data are obtained
from these measurements.
Exact Numbers
• Exact numbers have an infinite number
of significant figures.
• Exact numbers occur in simple counting
operations
12345
• Defined numbers are exact.
12 inches
100
centimeters
= 1 foot
= 1 meter
Form of a Measurement
numerical value
70.0 kilograms = 154 pounds
unit
Significant Figures
• The number of digits that are known plus
one estimated digit are considered
significant in a measured quantity
known
5.16143estimated
Significant Figures on
Reading a Thermometer
The
temperature
Temperature
is
oC is expressed
21.2
estimated
to be
oC. The last 2 is
to
3 significant
21.2
figures.
uncertain.
The
temperature
Temperature
is
oC is expressed
22.0
estimated
to be
to
3 osignificant
22.0
C. The last 0 is
figures.
uncertain.
The
temperature
Temperature
is
oC isto
22.11
expressed
estimated
be
oC. The last 1
to
4 significant
22.11
figures.
is uncertain.
Significant Figures
All nonzero numbers are significant.
461
Significant Figures
All nonzero numbers are significant.
461
Significant Figures
All nonzero numbers are significant.
3 Significant
Figures
461
Significant Figures
A zero is significant when it is between
nonzero digits.
3 Significant
Figures
401
Significant Figures
A zero is significant when it is between
nonzero digits.
5 Significant
Figures
93 . 006
Significant Figures
A zero is significant at the end of a number
that includes a decimal point.
5 Significant
Figures
55 . 000
Significant Figures
A zero is significant at the end of a number
that includes a decimal point.
5 Significant
Figures
2 . 1930
Significant Figures
A zero is not significant when it is before the
first nonzero digit.
1 Significant
Figure
0 . 006
Significant Figures
A zero is not significant when it is before the
first nonzero digit.
3 Significant
Figures
0 . 709
Significant Figures
A zero is not significant when it is at the end
of a number without a decimal point.
1 Significant
Figure
50000
Rounding
off Numbers
Rounding Off Numbers
• Often when calculations are performed
extra digits are present in the results.
• It is necessary to drop these extra digits
so as to express the answer to the
correct number of significant figures.
• When digits are dropped the value of
the last digit retained is determined by a
process known as rounding off
numbers.
Rounding Off Numbers
Rule 1. When the first digit after those you want to
retain is 4 or less, that digit and all others to its
right are dropped. The last digit retained is not
changed.
4 or less
80.873
Rounding Off Numbers
Rule 2. When the first digit after those you want to
retain is 5 or greater, that digit and all others to its
right are dropped. The last digit retained is
increased by 1.
drop
5 or
these
greater
figures
increase by 1
6
5.459672
Significant Figures
in Calculations
Multiplication or Division
In multiplication or division, the
answer must contain the same
number of significant figures as in the
measurement that has the least
number of significant figures.
2.3 has two significant
figures.
(190.6)(2.3) = 438.38
190.6 has four
significant figures.
Answer given
by calculator.
The answer should have two significant
figures because 2.3 is the number with
the fewest significant figures.
Round off this
digit to four.
Drop these three
digits.
438.38
The correct answer is 440 or 4.4 x 102
Addition or Subtraction
The results of an addition or a
subtraction must be expressed to the
same precision as the least precise
measurement.
The result must be rounded to the
same number of decimal places as
the value with the fewest decimal
places.
Add 125.17, 129 and 52.2
Least precise number.
Answer given
by calculator.
Round off to the
Correct answer.
nearest unit.
306.37
125.17
129.
52.2
306.37
Scientific Notation
of Numbers
• Very large and very small numbers are
often encountered in science.
602200000000000000000000
0.00000000000000000000625
• Very large and very small numbers like these
are awkward and difficult to work with.
A method for representing these numbers in a
simpler form is called scientific notation.
23
602200000000000000000000
6.022 x 10
-21
0.00000000000000000000625
6.25 x 10
Scientific Notation
• Write a number as a power of 10
• Move the decimal point in the original number
so that it is located after the first nonzero
digit.
• Follow the new number by a multiplication
sign and 10 with an exponent (power).
• The exponent is equal to the number of
places that the decimal point was shifted.
Write 6419 in scientific notation.
decimal after
first nonzero
digit
power of 10
1
2
3
6.419
641.9x10
64.19x10
6419.
6419
x 10
Write 0.000654 in scientific
notation.
decimal after
first nonzero
digit
6.54 x
0.000654
0.00654
0.0654
0.654
-4
-2
-1
-3
10
power of 10