# . . . Calculator Help

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## Basic Calculator Tips

Everyone knows that using a calculator simplifies solving numerical problems. However, some students will make mistakes and come up with incorrect results when using an unfamiliar calculator. If you expect to use a calculator on a test or a quiz, you should become comfortable with that particular model of calculator by using it for class and homework problems. It is not a good idea to borrow a calculator on the day of a test.

What follows are tips on avoiding the most common calculator mistakes. In the calculator scripts which follow, square brackets [ ] are used to indicate calculator keys. For example, entering the number 25 the calculator script would look like this: [2][5].

### Keys

Before you begin, locate the keys for each of the four basic mathematical operations: for addition [+] for subtraction [-]. For multiplication you may have either a star [*] or an x [x] and for division you may have the traditional division symbol [ ] or the slash [ / ]. In order to generate an answer you will use a key labeled either [=] or [ENTER].

Danger! Very common error #1

The subtraction key [-] must not be confused with another key which will be marked either[(-)] or [+/-]. That key is used to change the sign on a number or an exponent.

The fact that calculator keys do not always have the same label is further complicated by the fact that the symbol which is displayed may not correspond to the symbol on the key! For example, on some graphing calculators pushing the [x] key causes a * to be displayed. Since * and "x" both mean multiply in mathematical notation, these two symbols have the same meaning. You need to become familiar with the keys on your calculator in order to avoid these pitfalls.

For the purpose of this tutorial we will use [x] to indicate multiplication, [/] to indicate division, [EXP] for entering exponents, and [=] to indicate generating the answer.

Here is an example of the keys on the TI-34 calculator. Other examples are given below.

Danger ! Very common error # 2 . . . . Order matters !!

It can matter what order you enter a calculation if it involves multiple steps. Your calculator will typically do multiplication and division steps before doing addition or subtraction. You can force the calculator to do the part of the problem that you have entered by using the [=] key.

Problem 1.

Suppose you are given this problem: 1.23 + (4.56 - 6.7 / 8.7) x 9.1

Many calculators have parenthesis keys which will allow you to enter the problem as you see it.

One possible calculator script: [1][.][2][3][+][(][4][.][5][6][-][6][.][7][/][8][.][7][)][x][9][.][1][=]

Note that if you press the [=] key at other times in the problem you may get the wrong answer !

If you calculator does NOT have parenthesis keys, it is usually wisest to start by doing the calculation inside the parentheses first, pressing [=] and then doing the parts outside the parentheses.

Another possible calculator script: [4][.][5][6][-][6][.][7][/][8][.][7][=][x][9][.][1][=][+][1][.][2][3][=]

Possible WRONG answers (if you enter the problem incorrectly) are -1.22 or 8.95

### Entering Exponents

Entering exponents is done by pushing the key labeled [EXP] or [EE] or [EEX]. If you have a key labeled [ex] do not use that to enter exponents. It has a different function.

Danger! Very common error #3

If you are entering numbers in scientific (E) notation, you should enter the "x10" and the exponent by pushing ONLY the [EXP] key followed by the exponent. For example (2.5x103) should be entered as follows: [2][.][5][EXP][3].

It would be INCORRECT to enter it as [2][.][5][*][10][EXP][3].

Problem 2.

Multiply 2.5x103 times 3.32x106

Calculator script: [2][.][5][EXP][3][*][3][.][3][2][EXP][6][=]

Answer = 8.3E9 which might also look like 8.3 09 and would be written as 8.3 x 109.

To enter a negative exponent, after typing in the exponent use the [+/-] key to change the sign of the exponent. For example, 5.3 x 10-7 would be entered as [5][.][3][EXP][7][+/-].

### Mode

Calculators have various methods of displaying numbers. In FIXED mode there will always be a specific number of places after the decimal. For example, calculations with money may use FIXED mode with two places after the decimal. In SCIENTIFIC notation there will usually be a single digit followed by the decimal point, followed by more digits, the letter E and then more digits. The letter E tells you that what follows is the exponent on an (understood) 10 in the number. Some calculators do not show the letter E. They will just leave a space between the number and the exponent.

Examples:

2450 = 2.45x103 which would appear on the display as 2.45E03 or 2.45 03 or 2.45 03

0.0456 = 4.56x10-2 which would appear on the display as 4.56E-02 or 4.56 -02 or 4.56 -02

Problem 3.

Multiply 34.87 times 21.4

Calculator script: [3] [4] [.] [8] [7] [x][2] [1] [.] [4] [=]

Depending upon the MODE you have set, the answer may look like one of the following:

7.46218E2 (Scientific)

746.218 (Floating)

746.2 (Fixed 1)

### Angle Measurements

If you are doing problems involving trignometric functions (sine, cosine, tangent), you need to be concerned about how the angles are being measured. Frequently mathematics problems are done using radians. Science problems are frequently done using degrees. Most calculators can deal with either form of angle measurement. Which form is being used is another thing which is determined by the calculator's mode. This is usually indicated in small letters at the bottom of the display. If you see "DEG" then the calculator expects you to work in degrees. If you see "RAD" then you should be working in radians. To change the mode of the calculator from radians to degrees (or vice versa) push the [DRG].

Danger! Very common error #4

It is easy to forget that there are different ways to express angles when doing problems. If you are trying to solve a problem such as 100*sin(30o), but your calculator is using radians you will get an answer of -98.8, which is incorrect. The correct answer is 50.

Problem 4.

Find the cosine of 52 degrees.

Calculator script:

Check to make sure the calculator is in DEG mode. If not, push [DRG] until it is.

Then enter: [5][2][cos]

You probably do NOT need to press the [=] key in this case.

### Logarithms

Most calculators can do either base 10 or base "e" logarithms. The [log] button does base 10 logarithms. The[ln] button does base "e" logarithms.

Problem 5.

Find the base 10 logarithm of 546.2

Calculator script: [5][4][6][.][2][log]

Here is an example of the important keys on another type of scientific calculator.

## Other calculator tutorials on the Web:

HP 10B calculator: http://www.clarion.edu/cobweb1/calculat/calculat.htm

HP 38-G calculator: http://iq.orst.edu/math-help/hp38g/

TI-82 calculator: http://mtl.math.uiuc.edu/non-credit/basic82/

TI-82 calculator: http://www.utep.edu/region19/modules/gracal05/index.htm

TI-83 calculator: http://kings.k12.ca.us/math/lessons/ti83tutorial.html

TI-83 calculator: http://www.bashonline.com/resources/ti83.asp

TI-92 calculator: http://www-cm.math.uiuc.edu/mtl/TI92/index.htm

TI-92 calculator: http://mtl.math.uiuc.edu/non-credit/basic92/

Developed by the CU - Colorado Springs Department of Physics and Energy Science