1. Figure 1.9A
The number of significant figures in a measurement depends upon the measuring device.
32.330C
32.30C

2. Rules for Determining Which Digits are Significant
All nonzero digits are significant
Zeros in between two nonzero digits are significant
Zeros to the left of any nonzero digit are NOT significant
Zeros to the right of nonzero digits are significant if the number has a decimal point
Zeros that end a number and lie either after or before the decimal point are significant; thus ml has four significant figures, and 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!

3. 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.
(a) L
(b) g
(c) 53,069 mL
(d) m
(e) 57,600. s
(f) cm3

4. 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 mL mL
mL = mL
Example: subtracting two volumes mL mL
mL = mL

5. Multiply the following numbers:
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 cm
= cm3 = 23 cm3

6. 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.
rounds to 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.

7. 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.

8. Precision and Accuracy Errors in Scientific Measurements
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.

9. Precision and accuracy in the laboratory.
Figure 1.10
Precision and accuracy in the laboratory.
precise and accurate
precise but not accurate

10. Precision and accuracy in the laboratory.
Figure 1.10
continued
random error
systematic error

11. 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

12. 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.

13. Law of Mass Conservation:
The total mass of substances does not change during a chemical reaction.
total mass
total mass
reactant reactant 2
product =
calcium oxide carbon dioxide
calcium carbonate
CaO CO2
CaCO3
56.08g g
100.08g

14. Law of Definite (or Constant) Composition:
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)
Mass Fraction
(parts/1.00 part)
Percent by Mass
(parts/100 parts)
8.0 g calcium
2.4 g carbon
9.6 g oxygen
20.0 g
0.40 calcium
0.12 carbon
0.48 oxygen
1.00 part by mass
40% calcium
12% carbon
48% oxygen
100% by mass

15. 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
g O
g C =
57.1
42.9 =
1.33
g O
g C
72.7
27.3 = =
2.66
2.66 g O/g C in II
1.33 g O/g C in I 2 1 =