Each chapter is broken up into smaller, “digestible” units. Chapter 4 deals with using a
calculator such as the Texas Instruments, TI-84 Plus, which is commonly used for
chemistry. Section 4-4 on the Order of Operations and Using Parentheses (a common
source of errors for students) is shown as a sample lesson. Previous Chapters covered
algebra review and scientific notation.
Chapter 4 Using Your Calculator for Chemistry
50
4.1
Some important keys
4.2
Exponents and square roots
4.3
Float mode, Scientific notation and the EE Key
4.4
Order of operations and using parentheses
4.5
Logs and anti-logs for pH problems
4.6
The Periodic Table and other science applications
4.7
If your calculator is acting weirdly…
Graphing – see chapter 10
50
53
56
59
62
66
70
Section 4-4 Order of Operations and Using Parentheses
Calculators can’t think. They can only do EXACTLY what you tell them to do in the way they have
been programmed to do it. Students sometimes get the wrong answer just because they did not
enter the calculation into the calculator correctly. You can usually avoid this by using plenty of
parentheses. Let’s look at some examples.
Let’s say you want to get an answer to this problem with your calculator:
If you key in:
If you key in:
2
4
2
4
(-2)4 = 16
-16
Wrong! You did not put
parentheses around the -2 so
the calculator did this: -(2)4
ERR
OOPS! You used subtract (
instead of negative (
If you key in:
2
16
4
Correct!
Order of Operations
The order of operations is the same as you are used to:
Parentheses Exponents Multiplication/Division Addition/Subtraction
(Whichever comes first
going from left to right.)
Please
Excuse
My Dear
(Whichever comes first
going from left to right.)
Aunt Sally
)
)
THE MOST COMMON SOURCE OF ERRORS FOR STUDENTS
12 + 6
(2)(3)
What if you want to solve this problem:
Press:
12 6
You see:
12 + 6/2
2
3
3
21
Answer: 18 =
6
Press:
(12 6)
2
You see:
(12+6)/2 3
3
3
27
WRONG!
Order of operations says do
(12+6) first (parentheses), then 18/2 and
finally 9 x 3.
WRONG!
Order of operations says
do 6/2 first, then 3 x 3, and finally 12+9
To do it correctly…
Press:
(12
6)
(2
You see:
(12+6)/(2 3)
3)
3
CORRECT! Order of
operations says do (12+6),
then (2 x 3) and finally
18/6.
Biggest Problem
Failing to put parentheses around the numerator or
denominator leads to more problems than anything else.
This is because we don’t usually bother to do this when
we are writing equations by hand.
We usually write it by hand this way:
We need to put it in the calculator this way
(12 +6)
((2) (3))
GET USED TO USING PARENTHESES!
or
(12+6)
(2*3)
Another Correct Way
Here is another way to do this problem and get the correct answer:
Press:
(12
Press:
6)
2
3
In this case, the calculator is doing:
You see:
(12+6)/2
9
You see:
Ans/3
3
(12+6) = 9
2
and then:
9 =3
3
There is more than one CORRECT way to use your calculator to solve problems (and also many
INCORRECT ways ). You need to practice with the calculator and find your own correct techniques
to use. Try the following practice problems and make sure that you get the correct answers.
Check to see that your calculator is set on floating decimal and scientific notation modes for the
following problems.
Example Problems
Rewrite the problem to remind yourself how to put it in your calculator and then solve it.
1.
56 + 43
(7) (4)
Problems for you to solve (answers on page )
2.
4(34.5 – 23)
1.5 + 0.34
3.
1,3 (20)
6.3-8.3
4.
(5.4 + 2.93)(4-11)
(2)(-5)
5.
(52) (7- 10)
5,000
You do not always have to
do the whole problem in
one line on your calculator.
As calculations get
“messier”, it is perfectly
acceptable to do part of the
calculation, rewrite the
simplified equation and
start again
with the
calculator.
Now let’s add some scientific notation.
6.
2.1 x 10-4
7 x 103
7.
3.4 x 102 + 4.8 x 103
54.2 + 5.0858 x 103
8.
8 ( 9.5 x 106)
21.9 -1.9
9.
-41 + (√(60 + 21))
(8 X 10-3) ( 2 X 10-12)
Answers to all Problems are shown at the end of the book.
Section 4-4 Order of Operations and Using Parentheses
2.
2.5 x 101
3.
-1.31 x 101
4.
5.831
5.
-1.5 x 10-2
6.
3 x 10-8
7.
1
8.
3.8 x 106
9.
-2 X 1015