Chemistry 3A
Chapter 2 Lecture Overview
Sections 2.2 - 2.5
Fall 2010
Instructor: Williams, B.
Section 2.2 Scientific Notation: Writing Large and Small Numbers
1. Scientific Notation: An ordinary decimal number is expressed as a product of a number
between 1 and 10, multiplied by 10 raised to a power. It has two parts:
 Coefficient: A number between 1 and 10
 Exponential term: A power of 10, (× 10n)
2. To convert decimal numbers to scientific notation:
 The value of the exponent is equal to the number of places the original decimal must
be moved to give a coefficient between 1 and 10. If the decimal point moves left to
obtain the coefficient, the exponent is positive.
 If the decimal pt. moves right to obtain the coefficient, the exponent is negative.
 The coefficient must contain the same number of SF’s as present in the original
number.
3. Scientific Notation and Calculators
To enter a number into the calculator:
a)
b)
c)
d)
Enter the number (coefficient)
Push the EE or EXP key on calculator
Enter the value of the exponent
If the exponent is negative, use the ± key.
Do not use this sequence:
a) Enter the number
b) Push × , then enter 10
c) Enter EE key
Section 2.3 Significant Figures: Writing Numbers to Reflect Precision
1. Two types of numbers:
 Counted (exact)
 Measured (not exact)
Since it is not possible to measure anything exactly, there is always a certain amount of
uncertainty involved in every measurement. So, every measured number has some
degree of uncertainty.
2. Counting Significant Figures
Significant Figures: All digits known with certainty plus one digit that is uncertain.
It is understood that uncertainty in the last digit is plus or minus one unit. For this course
only one estimated digit is ever recorded.
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3. Rules for Counting Significant Figures
To interpret significance of a reported measurement, it is important to count the SF’s in a
number because they affect the answers that are stated in calculations. Zeros may or
may not be significant depending on how they were used.
 Nonzero digits are always significant.
 Zeros may or may not be significant; it depends on its location in a sequence of
digits.
o Leading zeros precede all nonzero digits and never count as SF’s. They are only to
indicate the position of the decimal point.
o Captive zeros are between nonzero digits and always count as SF’s.
o Trailing zeros are at the end of number. They are significant only if a decimal point
is present in a number. A decimal point placed at the end of a number makes all of
the trailing zeros significant.
4. Exact Numbers
An exact number has no uncertainty. Therefore, it has an unlimited amount of SF’s. This
includes:
 Counting numbers
 Conversions between units within the English system
 Conversions between units within the Metric system
 Conversions between the English and Metric system are generally not exact.
Exceptions include: 1 in = 2.54 cm, 1 lb = 454 g (exactly)
Section 2.4 Significant Figures in Calculations
1. The calculated answer should not be more or less precise than the measured quantities
used in the mathematical operation.
2. Rounding
Rounding (off) is the process of deleting unwanted (non-significant) digits from a
calculated number. The number of SF’s in the measured number will limit the number of
SF’s in the calculated answer.
Rules for rounding off digits
If the first digit to be dropped (leftmost) is 4 or less, the preceding digit remains the same.
If the first digit to be dropped (leftmost) is 5 or more, the preceding digit is increased by
one.
3. Multiplication and division
In multiplication or division, the product or quotient (answer) can have no more SF’s than
the number with the smallest number of SF’s.
4. Addition and subtraction
In addition or subtraction, the sum or difference can have no more places after the
decimal than there are in the number with the smallest number of digits after the decimal.
5. Calculations Involving both Multiplication/Division and Addition/Subtraction (See
page 20-21 in text)
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Section 2.5 The Basic Units of Measurement
1. All measurements contain:
 A number that tells the quantity being measured.
 A unit that gives the nature of the quantity being measured. A unit is a label to
describe what is being measured or counted.
2. The two formal systems are:
 The English (U.S.) system which includes the foot, pound, quart, gallon.
 The metric system which is used daily (worldwide). However, it is used in the U.S.
mainly for scientific work.
3. The metric system is a decimal based system of measurement. It is the most commonly
used system of measurement.
 There is one basic unit for each type of measurement: length, volume and mass.
 There is the traditional metric system and the SI system which is a modern variation of
the metric system based on the choice of fundamental (base) units.
4. Here are the fundamental units of the metric system:
 The base unit of length in the metric system is the meter. It is about the same size as
the English yard unit: 1 meter = 1.09 yards
 The gram is the base unit of mass in the metric system. It is much smaller than the
English pound and the ounce: 454 g = 1 lb
 A liter is the base unit of volume in the metric system. It is equal to the volume
occupied by a cube that is 10 cm on each side: 1L = 1.06 quart
 The SI system is a recent modification of the metric system. Its most common base
units are kilogram, meter, and the second.
5. Prefix multipliers
 In the metric system there is one basic unit for each type of measurement (i.e., length,
volume, and mass).
 Each basic unit is multiplied by a power of ten to form larger or smaller units.
 Each of the larger or smaller units is named by attaching the prefix that indicates the
particular power of ten that is involved (See table 2.2 on page 23 or handout given in
class).
 In each table is given the symbol or abbreviation and the corresponding appropriate
power of ten.
6. Derived Units
 A derived unit of measurement comes from combining one or more measurements;
these units come from basic units such as length and time.
 For example, miles per hour or kilometers per hour, involves combining units.
 Volume measures the amount of space contained within a three-dimensional shape. It
is derived from units of length multiplied by itself three times giving cubic units.
 in3, ft3, m3, and cm3 (use cm3 for solids and mL for liquids)
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