Calculator Guidelines

CALCULATOR GUIDELINES

Copyright by Ingrid Stewart, Ph.D. Please Send Questions and Comments to ingrid.stewart@csn.edu.

What is discussed in this lecture?

1. The Order of Operations
2. TI 30X IIB and IIS Calculator Examples

1. Order of Operations

The Order of Operations is a set of rules that tells us in which order to perform mathematical operations in an expression. This allows each and every person to interpret a mathematical expression in the same way.

Rule:

First, carry out operations in numerators and denominators of fractions and within radicals. We might have to use steps two through five!

Then carry out operations enclosed by grouping symbols, such as parenthesis ( ), brackets [ ], and braces. Note that the value enclosed by the innermost symbol is done first. The innermost symbol is usually a set of parentheses.

Exponential expressions are evaluated next.

Then we multiply and divide in order from left to right.

Lastly we add and subtract in order from left to right.

Example 1:

Use the Order of Operations to simplify 5² 6(3) (5 + 4).

We'll do the addition within parentheses first.

5² 6(3) 9

Next, we'll evaluate the exponent.

25 6(3) 9

Now, we have to multiply and divide IN ORDER from left to right. We'll do the multiplication first!

25 18 9

Then, we'll do the division.

25 2

Finally, we'll subtract to get 23.

2. TI 30X IIB or IIS Calculator Examples

You may use only a scientific and NOT a graphing calculator for all assignments including quizzes and exams. Calculators use the Order of Operations. Sometimes you must tell the calculator the correct order in which you want your calculations be done by using the parenthesis buttons as appropriate.

The calculator recommended in the syllabus for this class is the Ti 30X IIB or IIS. Beware ... if you have a calculator that uses "reverse logic", for example the Ti 30Xa, some math problems are pretty much impossible to do.

Example 2:

Evaluate the exponential expression using the caluclator.

We can find second powers in two different ways.

We simply press the caret ^ button on the calculator. It is used to indicate "raising to a power."

We find that

There is also an button to strictly evaluate second powers.

We find that

Example 3:

Evaluate the exponential expression using the calculator.

To find any other power, we must strictly use the caret ^ button.

We find that

Example 4:

Evaluate the exponential expression using the calculator.

We must use the input the parenthesis button! You will soon see that without them your answer will be different.

Warning: We must use the (-) button on the calculator to indicted a negative sign. We CANNOT use the subtraction button.

We find that

Example 5:

Now let's evaluate the exponential expression using the calculator.

We must use the input the parenthesis button! You will see that without the parentheses your answer will be different from the one in Example 4 above.

Warning: We must use the (-) button on the calculator to indicted a negative sign. We CANNOT use the subtraction button.

We find that

Example 6:

Let's compare to one more time.

Note: is NOT equal to . To indicate that we want to raise a negative number to a power, we are required to use parentheses!!!!!

actually means

Then .

Note: Here we have to use the Order of Operations rule that requires us to evaluate exponents before multiplication.

Example 7:

Evaluate the number (Pi) using the calculator. Examining any calculator, we will find that there is a button. To find out the value of , we input the following into most calculators:

We find that

Note: The calculator actually does not tell us that has infinitely many decimal places. That is, it is an irrational number. The calculator simply fills up all available slots on its screen with decimal places. YOU must know that the number is an irrational number with decimal places that go on to infinity.

Example 8:

Evaluate the number using the calculator.

Examining any calculator, we find that there is NO button containing the number . However, we can find the picture over the LN button. This means that we must use the 2nd button to access the number .

To find out the value of , we input the following:

Note that we used the power of 1 to find the value of the number .

Warning: A left parenthesis will open when we activate , specifically we will see . The calculator is now waiting for us to to input an exponent. After we type a desired number, we MUST press the right parenthesis button to close the set of parentheses.

We find that

Note: The calculator actually does not tell us that has infinitely many decimal places. That is, it is an irrational number. The calculator simply fills up all available slots on its screen with decimal places. YOU must know that the number is an irrational number with decimal places that go on to infinity.

Example 9:

Evaluate using the calculator.

We will use the function (2nd and LN allows us to access it) and the power ^ button on the calculator.

Note: We will always use the function of the calculator and not 2.72.

Note: We must insert the right parenthesis because when using the buttons 2nd and LN a left parenthesis will open automatically.

We find that

Example 10:

Evaluate using the calculator.

We press the 2nd button and then the button.

Warning: Left parenthesis will open after we press , specifically we will see . After we type in the radicand, we MUST press the right parenthesis button before we press ENTER button.

We find . Note is an irrational number. It has infinitely many decimal places. The calculator only shows a finite amount.

Example 11:

Evaluate using the calculator.

First we type the index 3 and then we press the 2nd button followed by the caret ^ button.

We find that . Note that is an irrational number. It has infinitely many decimal places. The calculator only shows a finite amount.

Example 12:

Evaluate using the calculator.

We will use the parenthesis ( ) buttons and the caret ^ button ("raising to a power") on a calculator to do the entire calculation.

We find that

Example 13:

Evaluate using the calculator.

We will use the parenthesis ( ) buttons and the caret ^ button on a calculator to do the entire calculation.

We find that

Example 14:

Evaluate using the calculator.

We will use the parenthesis ( ) buttons and the caret ^ button on a calculator to do the entire calculation.

We find with the three dots (ellipsis) indicating infinitely many decimal places.

Example 15:

Evaluate using the calculator.

We will use the parenthesis ( ) buttons and the caret ^ button on a calculator to do the entire calculation.

We find that

Example 16:

Evaluate using the calculator.

We will use the parenthesis ( ) buttons and the caret ^ button on a calculator to do the entire calculation.

NOTE: We must open two left parenthesis to tell the calculator to raise the fraction to the power of 420. Without the second parenthesis the calculator would have only raised 12 to the 420th power due to the Order of Operation!

Incidentally, the calculator does not have a brackets [ ] buttons, that's why we have to use a second set of parentheses!

After we press the ENTER button, we immediately press

NOTE: As soon as we do so, the value on the calculator will change to ANS.

Then we continue as follows:

We find that with the three dots (ellipsis) indicating infinitely many decimal places.

Example 17:

Evaluate using the calculator.

We will use the parenthesis ( ) buttons and the caret ^ button on a calculator to do the entire calculation.

Calculator Input - Numerator:

After we press the ENTER button, we immediately press.

NOTE: As soon as we do so, the value on the calculator will change to ANS.

Then we continue as follows:

Calculator Input - Denominator

NOTE: We must open two left parenthesis to tell the calculator to raise the fraction to the power of 216. Without the second parenthesis the calculator would have only raised 12 to the 216th power due to the Order of Operation!

We find that with the three dots (ellipsis) indicating infinitely many decimal places.

Example 18:

Evaluate using the calculator.

Input the expression into your calculator with parentheses around the numerator to tell the calculator that it must first add the terms in the numerator.

That is, input

Had you input , the calculator would have done “division before addition” and would have only divided the square root by 2 .