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Figure 1.9A
The number of significant figures in a measurement depends
upon the measuring device.
32.330C
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32.30C
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Rules for Determining Which Digits are Significant
All digits are significant
except zeros that are used only to position the
decimal point.
•Make sure that the measured quantity has a decimal point.
•Start at the left of the number and move right until you reach the first
nonzero digit.
•Count that digit and every digit to it’s right as significant.
Zeros that end a number and lie either after or before the decimal
point are significant; thus 1.030 ml has four significant figures,
and 5300. L has four significant figures also.
Numbers such as 5300 L are assumed to only have 2 significant
figures. A terminal decimal point is often used to clarify the
situation, but scientific notation is the best!
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Sample Problem 1.7
Determining the Number of Significant Figures
PROBLEM: For each of the following quantities, underline the zeros that are
significant figures(sig figs), and determine the number of
significant figures in each quantity. For (d) to (f), express each
in exponential notation first.
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(a) 0.0030 L
(b) 0.1044 g
(c) 53,069 mL
(d) 0.00004715 m
(e) 57,600. s
(f) 0.0000007160 cm3
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Rules for Significant Figures in Answers
1. For addition and subtraction. The answer has the
same number of decimal places as there are in the
measurement with the fewest decimal places.
Example: adding two volumes
83.5 mL
+ 23.28 mL
106.78 mL = 106.8 mL
Example: subtracting two volumes
865.9
mL
- 2.8121 mL
863.0879 mL = 863.1 mL
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Rules for Significant Figures in Answers
2. For multiplication and division. The number with the least
certainty limits the certainty of the result. Therefore, the answer
contains the same number of significant figures as there are in the
measurement with the fewest significant figures.
Multiply the following numbers:
9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm3 = 23 cm3
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Rules for Rounding Off Numbers
1. If the digit removed is more than 5, the preceding number
increases by 1.
5.379 rounds to 5.38 if three significant figures are retained
and to 5.4 if two significant figures are retained.
2. If the digit removed is less than 5, the preceding number is
unchanged.
0.2413 rounds to 0.241 if three significant figures are retained
and to 0.24 if two significant figures are retained.
3. Be sure to carry two or more additional significant figures
through a multistep calculation and round off only the final
answer.
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Issues Concerning Significant Figures
Electronic Calculators
be sure to correlate with the problem
FIX function on some calculators
Choice of Measuring Device
graduated cylinder < buret ≤ pipet
Exact Numbers
60 min = 1 hr
numbers with no uncertainty
1000 mg = 1 g
These have as many significant digits as the calculation requires.
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Precision and Accuracy
Errors in Scientific Measurements
Precision Refers to reproducibility or how close the measurements are to each
other.
Accuracy Refers to how close a measurement is to the real value.
Systematic Error Values that are either all higher or all lower than the actual value.
Random Error In the absence of systematic error, some values that are higher and
some that are lower than the actual value.
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Figure 1.10 Precision and accuracy in the laboratory.
precise and accurate
precise but not accurate
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Figure 1.10
continued
Precision and accuracy in the laboratory.
random error
systematic error
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Definitions for Components of Matter
Element - the simplest type of substance with unique physical and
chemical properties. An element consists of only one type of atom. It
cannot be broken down into any simpler substances by physical or
chemical means.
Molecule - a structure that consists of two or
more atoms that are chemically bound together
and thus behaves as an independent unit.
Figure 2.1
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Definitions for Components of Matter
Compound - a substance
composed of two or more elements
which are chemically combined.
Figure 2.1
Mixture - a group of two or more
elements and/or compounds that
are physically intermingled.
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Law of Mass Conservation:
The total mass of substances does not change during a chemical
reaction.
reactant 1
+
product
reactant 2
total mass
=
calcium oxide
+
carbon dioxide
CaO
+
CO2
total mass
calcium carbonate
CaCO
3
56.08g
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+
44.00g
100.08g
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Figure 2.2
Law of Definite (or Constant) Composition:
No matter the source, a particular compound is
composed of the same elements in the same parts
(fractions) by mass.
Calcium carbonate
Analysis by Mass
(grams/20.0g)
8.0 g calcium
2.4 g carbon
9.6 g oxygen
20.0 g
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Mass Fraction
(parts/1.00 part)
Percent by Mass
(parts/100 parts)
0.40 calcium
0.12 carbon
0.48 oxygen
40% calcium
12% carbon
48% oxygen
1.00 part by mass
100% by mass
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Law of Multiple Proportions:
If elements A and B react to form two compounds, the different
masses of B that combine with a fixed mass of A can be expressed
as a ratio of small whole numbers.
Example: Carbon Oxides A & B
Carbon Oxide I : 57.1% oxygen and 42.9% carbon
Carbon Oxide II : 72.7% oxygen and 27.3% carbon
Assume that you have 100g of each compound.
In 100 g of each compound: g O = 57.1 g for oxide I & 72.7 g for oxide II
g C = 42.9 g for oxide I & 27.3 g for oxide II
gO
gC
57.1
=
gO
gC
42.9
72.7
=
27.3
= 1.33
= 2.66
2.66 g O/g C in II
1.33 g O/g C in I
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=
2
1