Download Using Your Calculator

ASTR 1030 Astronomy Lab
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Using Your Calculator
USING YOUR CALCULATOR
Calculator Rule #1:
Don't switch off your brain when you switch your calculator on! Your calculator is intended to
eliminate tedious arithmetic chores, not to do your thinking for you. It's very easy to accidentally
press the wrong buttons. Before you write down any answer, ask yourself if the answer seems
reasonable. Intelligent use of your calculator will make your success in this course far more likely!
Example: Suppose you punch in the following: (3.28 x 104) x (2.4 x 10-7). Since 3 x 2 = 6, and
(104) (10-7) = 10-3, you know that your answer should be near 6 x 10-3. If your calculator gives
you the answer 2.3 x 1015, then you would know you have done something wrong and should try
again.
Example: Suppose you punch in: 47 . Since 47 is between 36 and 49, and you know that 36
= 6 and 49 = 7, you know that your answer should be between 6 and 7. If your calculator gives
you the answer 8.3, then you would know you have made an entry error and should try again.
Variations among Calculators:
Most scientific calculators have keys to perform all of the operations described below. However,
the labeling of the keys on your calculator, and the sequence in which they must be pushed, may
differ slightly from the examples given here. If you cannot get your calculator to do all the
operations in these examples, ask your instructor for assistance.
Scientific Notation:
Your calculator should have a key for entering scientific notation. It probably is labeled either EXP
or EE (for "exponent" or "enter exponent") . This key is used to enter the power of 10
multiplying the number you have entered previously. For example, to enter the number 3.5 x 106
you would use the key sequence:
3.5 EE 6
Note that the EE key can be thought of as meaning "times 10 to the power that I enter next".
Thus, you must be especially careful in entering powers of 10, since there must be a preceding
number for you to multiply "times 10 to the power of ..." with. For example, to enter the number
108 you would press:
1 EE 8
.
A common mistake is to enter: 10 EE 8 . Note that this means 10 x 108 or 109.
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Most calculators are a bit tricky in the way you must enter a negative exponent. If you want to
enter 5 x 10-3, for example, you do not press 5 EE -3 = ; the calculator will probably
perform the operation (5 x 100) - 3 = 2. Instead, you must use the "change sign" key, +/- or
CHS , which toggles the sign between positive and negative values (check the display to see if the
exponent is correct):
5 EE +/- 3 =
or
5 EE 3 +/- =
Switching Between "Normal" and Scientific Notation:
Most calculators have a single key which switches between scientific and "normal" notation. The
labeling of this key varies significantly among calculators, but often includes the letters "F" and "E"
(which stand for "floating point notation" and "exponential notation", respectively). A common
label for this key is F-E . On some calculators a sequence of keys must be used instead of a
single key. On Sharp brand calculators, for example, the key is labeled FSE ; you may have to
press this key more than once. On the Casio fx-250, notation is changed by using the MODE
key:
MODE 82
MODE 84
gives you scientific notation with 2 significant figures.
gives you scientific notation with 4 significant figures.
To convert to normal notation, press MODE 9 .
Angles and Trigonometry
Your calculator should have keys for all of the standard trigonometric functions including sin, cos,
tan, and their inverse operations: arcsin, arccos, and arctan.
Using the keys for the trigonometric functions is straightforward, except for one complication: the
trig functions are derived from work with angles, and there is more than one system for measuring
angles. Besides degrees, angles can also be measured in radians (common in math and science)
and in grads (common in engineering). Unless you tell your calculator in advance which type of
angle measurement you are using, your answer may come out incorrect.
Most calculators have a key labeled DRG which switches the calculator between degrees, radians,
and grads; usually, the numerical display has a label showing which mode is in effect. Before using
any trigonometric function, always put your calculator into the correct mode! In this lab course, if
you see the ° symbol, you will know to work with degrees, otherwise you should assume we are
working with radians.
For example, to calculate the sine of 45°, first make sure your calculator is in degree mode, and then
enter: 45 sin = . You will get the answer 0.707 (to 3 decimal places). Now switch your
calculator to radian mode, and find the sine of 45 radians with the same sequence of keys. You
should find that sin 45 = 0.851, demonstrating the importance of setting the mode before starting a
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Using Your Calculator
problem! (Note: it is not necessary to distinguish between these types of angle measure if you are
not using any trigonometric functions.)
If you know that the tangent of an unknown angle equals 0.235, for example, and you want to know
what the angle itself must be, you should press the inverse function key (usually labeled arc or
INV ) before selecting the trigonometric function:
.235 arc tan =
to get the answer 13.22° or 0.2308 radians (depending upon the angular mode the calculator was
in). Some calculators combine the inverse trigonometric function into a single key, such as tan-1 ;
you may have to press a "shift key" on your calculator to access it.
Powers and Roots:
Your calculator should have keys for raising numbers to powers or for taking roots. To raise a
number to a power, use the key which is usually labeled as yx or xy . For example, to do 53
you would use the following sequence of keys:
5 yx 3 =
and get the answer 125.
Many people are reluctant to use the "to the power of" key because they don't remember whether
the base number or the exponent should be entered first. If you find yourself in this situation,
here’s a simple test you can do to figure it out: enter the sequence 2 yx 1 = , and note the
result. If the answer is "2", then the base number comes first, because the calculator performed the
operation 21 = 2. If the answer is "1", then the exponent comes first, since 12 = 1.
x
To take roots, you use the key usually labeled
y
or
y
x
or x1/y . For example, to take the
4
4th root of 16 ( 16 or 161/4) you would use the keys:
16
x
y 4 =
and get the answer 2. If your calculator doesn't have a "root" key, you can get the same answer by
using the "power" key sequence:
16 yx .25 =
since 160.25 = 161/4 =
4
16 .
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Using Your Calculator
Reciprocals, Squares, Square Roots:
Reciprocals, squares, and square roots, can all be done using the "power" and "root" keys described
above. For example, to get the reciprocal of 25 you could enter the calculator equivalent of 25-1:
25 yx +/- 1 =
and get the answer 0.04 (which is 1/25). To square a number, you can use the "power" key and an
exponent of "2"; To get the square root, you can use the power key with an exponent of "0.5", or
the "root" key and a root of "2".
To make your life simpler, however, most calculators have special keys for taking squares (key
labeled x2 ), square roots (key labeled
), and reciprocals (key labeled 1/x
Some calculators also have special keys for cubes x3 and cube roots
For example, to calculate 382 you would enter: 38
x2
=
).
.
and get the answer 1,444. To
25 1/x =
calculate the decimal equivalent of 1/25, you would enter
3
or x-1
and get the answer 0.04.
You can even use the square root key twice to find the fourth root of a number, since the square root
of a square root is the fourth root: for example, you could find that 3 is the fourth root of 81:
4
1/2
81
= (81)
1/4
= (
811/2
)
=
81
by keying in the sequence
81
=
Pi (π):
The key labeled π can be used to automatically enter the numerical value of π. Simply press the π
key to see that π = 3.141592654 (to 9 decimal places).
Logarithms
You probably won't be doing any logarithms in this course, but since scientific calculators come
equipped with this capability, we will mention them very briefly. To take the common logarithm of
a number (to find out what power that 10 must be raised to in order to equal that number), use the
log key; for example, 50 log will produce an answer of 1.699, showing that 101.699 = 50. To
perform the inverse operation (to find out what number you would get if you raised 10 to a
particular power), you use the INV log or 10x keys.
Finally, there is the mysterious ln or lnx key, which performs what is known as a "natural"
logarithm. It works like a "common" logarithm, except that the base is the number e =
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2.718281828459 instead of 10. Believe it or not, the number e is as important to science and
mathematics as the number π. However, if you aren't overly fond of these subjects, you won't have
to worry about this key or its inverse ex either.
The Parentheses Keys:
All calculators have a priority system for performing operations. For example, multiplication has a
higher priority than addition, so that if you enter the key sequence:
5 +
3 x 2 =
the calculator will first multiply 3 x 2 = 6 and then add the 5 to get 11 (as opposed to first adding 5
+ 3 to get 8 and then multiplying by 2, which would give 16.) When performing calculations
involving multiple steps, you can get incorrect answers if you are not careful to understand your
calculator's priority system. You often can avoid problems, however, by making judicious use of
the keys ( and ) (if your calculator has them) to group your operations. For example, if you
wished to alter the priority of the above calculation, you could enter:
( 5 +
3 ) x 2 =
which will give you the answer 16.
Of course, if you are uncomfortable with long numerical calculations and want to make sure that
your calculator doesn't do something that you didn't intend for it to do, you can simply perform the
mathematical operations one at a time in the correct sequence, write down the intermediate answers,
and re-enter the needed numbers when appropriate. It may not be the most elegant use of your
calculator, but who cares, as long as you get what you wanted!