Download 4 Key Math Skills GOB Structures

1.4 Key Math Skills for Chemistry
A graph
represents the
relationship
between two
variables.
Learning Goal Review math concepts used in chemistry:
place values, positive and negative numbers,
percentages, solving equations, interpreting graphs, and
writing numbers in scientific notation.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
A. Identifying Place Values
For any number, we can identify the place value for each
of the digits in that number.
The place values for two numbers are listed below:
A premature baby has a
mass of 2518 grams.
A silver coin has a
mass of 6.407 grams.
Key Math Skill Identifying Place Values
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
B. Using Positive and Negative Numbers in Calculations
A positive number is any number that is greater than zero
and has a positive sign (+). Often the positive sign is
understood and not written in front of the number.
A negative number is any number that is less than zero and
is written with a negative sign (−).
Key Math Skill Using Positive and Negative Numbers in
Calculations
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Multiplication and Division: Positive and Negative Numbers
1. When two positive numbers or two negative numbers are
multiplied or divided, the answer is positive (+).
2. When a positive number and a negative number are
multiplied or divided, the answer is negative (−).
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Addition: Positive and Negative Numbers
1. When two positive numbers are added, the answer is
positive.
2. When two negative numbers are added, the answer is
negative.
3. When a positive number and a negative number are
added, the smaller number is subtracted from the larger
number and the result has the same sign as the larger
number.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Subtraction: Positive and Negative Numbers
When two numbers are subtracted, change the sign of the
number to be subtracted and then follow the rules for addition.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Calculator Operations
On your calculator, there are four keys used for basic
mathematical operations.
The change sign key is used to change the sign of a number.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Calculator Operations—Example
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
C. Calculating Percentages
To determine a percentage, divide the parts by the total
(whole) and multiply by 100%.
If the percentage of red balls is 5, it means there are 5 red
balls in every 100 balls.
Key Math Skill Calculating Percentages
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
D. Solving Equations
Equations can be rearranged to solve for an unknown variable.
1. Place all like items on one side.
2. Isolate the variable you need to solve for.
3. Check your answer.
Key Math Skill Solving Equations
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Solve the following equation for P1.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Solve the following equation for P1.
To solve for P1, divide both sides by V1.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
E. Interpreting Graphs
A graph
•
represents the relationship between two variables.
•
contains two perpendicular axes.
•
has a horizontal axis, or x axis.
•
has a vertical axis, or y axis.
Key Math Skill Interpreting Graphs
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Interpreting Graphs
In the following graph, the
• volume of a gas in a balloon is plotted against its
temperature.
• y axis represents the volume (L) of the gas in the balloon.
• x axis represents the temperature (°C) of the gas.
• title indicates that the volume of the balloon was
measured at different temperatures.
• points represent the volume of gas that was measured at
a specific temperature.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Interpreting Graphs
The line on the graph
• indicates a direct
relationship: that the
volume of a gas in a
balloon increases
with increasing
temperature.
• can be used to
determine the gas
volume at various
temperatures.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
F. Scientific Notation
People have an average of 1 × 105 hairs on the scalp.
Each hair is about 8 × 10−6 m wide.
Key Math Skill Writing Numbers in Scientific Notation
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Scientific Notation
Numbers written in scientific notation have two parts:
Coefficient
Power of 10
To write 2400 in the correct scientific notation,
• the coefficient is 2.4.
• the power of 10 is 3.
• write the product of the coefficient multiplied by a power
of 10.
2.4 × 103
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Scientific Notation
2 400
= 2.4 × 1 000
 3 places
0.00086 =
4 places 
=
2.4 × 103
Coefficient × Power
of 10
=
8.6 × 10−4
Coefficient × Power
of 10
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Some Positive Powers of 10
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Some Negative Powers of 10
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Measurements in Scientific Notation
Diameter of chickenpox virus
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
= 0.000 000 3 m
= 3 × 10−7 m
© 2016 Pearson Education, Inc.
Some Measurements Written in Scientific Notation
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Scientific Notation and Calculators
Numbers in scientific notation can be entered into a
calculator using the EXP or EE key.
The calculator display shows a number between 1
and 10 followed by a space and the power of 10.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Writing a Number in Scientific Notation
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Write each of the following in correct scientific notation:
A. 64 000
B. 0.021
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Write each of the following in correct scientific notation:
A. 64 000
STEP 1 Move the decimal point to obtain a coefficient
that is at least 1 but less than 10.
6.4
STEP 2 Express the number of places moved as a
power of 10.
104
STEP 3 Write the product of the coefficient multiplied
by the power of 10.
6.4 × 104
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Write each of the following in correct scientific notation:
B. 0.021
STEP 1 Move the decimal point to obtain a coefficient
that is at least 1 but less than 10.
2.1
STEP 2 Express the number of places moved as a
power of 10.
10−2
STEP 3 Write the product of the coefficient multiplied
by the power of 10.
2.1 × 10−2
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Concept Map
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.