MATH1015
1
WORKING WITH NUMBERS AND
EXPRESSIONS
PART 1: INTRODUCTION AND EXPLORATION
To get you started, here is a table of some of the basic math symbols you may encounter
SYMBOL
MEANING
EXAMPLE
x 2 means x has a value of 2
Equal
greater than
x > 2 means x is bigger than 2
less than
x < 2 means x is smaller than 2
greater than or equal to x 2 means x is bigger than or equal to 2
less than or equal to
x 2 means x is smaller than or equal to 2
x 2 means that x cannot be 2
not
equal
x 2 means that x has a value of approximately 2
approximately equal
x 2 means that x has a value of 2 or a value of
plus or minus
-2
proportional
f ( x ) x means that the function f (x ) is
proportional to the function x (i.e. f (x ) is a
multiple of x)
Infinity
n
nth root
a
y means that y is getting larger without
bound (i.e. goes off to infinity)
3
8 2 means that the cube root of 8 is 2. (i.e.
1
8 3 2)
Steps in Performing Mathematical Calculations:
read the problem carefully and make sure you understand it
determine the principles and relationships involved
determine what results are to be produced by the calculations
think about possible solution methods
include your intermediate stages of calculations
recognize different forms of the same value
pay special attention to writing the decimal place and including units
if possible, you should always mentally estimate an answer at the start of the
problem, and you should compare your final answer to this value
[Source: Modified from “Laboratory Mathematics: Medical and Biological Applications” by Campbell and Campbell, 1997]
Additional Notes:
MATH1015
2
Discussion questions:
How can we easily write the diameter of Jupiter and the size of an amoeba in
metres?
If we add 0.00001 to 10.3, is it correct to say that the answer is 10.30001?
Suppose we graph a set of data…what’s wrong with the following graph?
Is x 2 4 the same as x 2 ? What are 3 different ways that we can check
this?
Additional Notes:
PART II: PRE-LECTURE VIDEOS
Watch the pre-lecture videos to learn more about:
Order of operations
Rounding
Interval notation
Converting between a decimal, percent, and fraction
Scientific Notation
Significant figures
Graphing
Simplifying, expanding and factoring
MATH1015
3
Significant Figures: The following rules are used to help determine the number of
significant figures.
all non-zero figures are significant
zeros at the beginning of a number are not significant
zeros within a number are significant.
zeros at the end of a number after the decimal point are significant
and
when adding or subtracting, final answer has same number of decimal places as
the number in the question with the least decimal places
when multiplying or dividing, final answer has same number of sig figs as the
number in the question with the least sig figs
Video Notes
MATH1015
4
Video Notes
Extra Practice: Want more practice before the quiz? Check out:
Text #1: Sections 1.1, 1.2, 1.4, 1.5
PART 1II: APPLICATIONS AND ADDITIONAL PRACTICE
Example #1 (Order of operations and rounding): The Blood Alcohol Concentration
(BAC) of a man who has been drinking is a unitless quantity approximated by:
Number of oz % alcohol 0.075 body weight in lb – hr of drinking 0.015.
Find the BAC to the nearest thousandth (ignore sig fig) for a 190-lb man who, in 2 hr, has
ingested four 12-oz beers, each having a 3.2% alcohol content. [Answer: 0.031]
[Source: Modified from Precalculus by Margaret L. Lial, John Hornsby, and David I. Schneider, 4th ed, 2009.]
Example #2 (Scientific Notation + Sig Fig): A sodium chloride solution was prepared
in the following manner:
• A 25.0 mL volumetric flask was placed on an analytical balance and found to have a
mass of 35.6783 g.
• Sodium chloride was added to flask and the mass of the solid + flask was 36.2365 g.
• The flask was filled to the mark with water and mixed well.
Calculate the concentration of the sodium chloride solution in units of g/mL and give the
answer in scientific notation with the correct number of significant figures.
[Source: Chemistry by John E. McMurry, 7th ed, 2016.]
MATH1015
5
Example #3 (Order of operations and basic algebra): Explain algebraically why the
following trick always works: “Write down a positive number. Add 4 to it. Multiply the
result by the original number. Add 4 to this result, and then take the square root.
Subtract the number with which you started. The answer is 2”.
[Source: Contemporary Precalculus: A Graphing Approach by Thomas W. Hungerford and Douglas J. Shaw, 5th ed, 2009.]
Class Work:
0
