FAQs FOR SCIENTIFIC CALCULATORS
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Index:
(1) What's the best scientific calculator to buy, and where's the best
place to buy one?
(2) How do you do fractions on a scientific calculator?
(3) How do you do mixed numbers on a scientific calculator?
(4) My calculator has second power and third power, but how do you raise
to a higher power such as 6?
(5) I know what the EXP on my calculator is, but what's the ENG for?
(6) What's the x^{-1} on my calculator for?
(7) How do I change base of logs on a calculator?
(8) I often get the wrong answer when I enter an expression with several
operations. Why?
(9) What's the reason for parentheses on my calculator?
(10) How do I find what the angle whose cos is 0.5?
(11) I see the letters AOS and EOS on calculator
sheets. What do they mean?
(12) What are the parentheses for on a Casio Scientific calculator?
(13) When I enter (-32)^(1/5); then (-2)^3 I get a correct answer, -8,
but when I enter (-32)^(3/5) I get Ma ERROR. Why?
(14) My brother gave me an expensive calculator, HP-42S, without a book. I
can't even add on it. Can you help?
(15) What does S-V.P.A.M. on the Casio scientific calculator s mean?
(16) Will the Casio fx-7400G do fractions?
Answers:
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DISCLAIMER: The FAQs on this web site, and
especially particular FAQ #1 here, reflect the writer's subjective opinion and
observations. The FAQs should be considered only as another source of
information. The writer is not endorsing any particular brand or model of the
calculators mentioned or any particular store or shop. The writer does not
warrant the accuracy of any FAQ. Any calculator mentioned may not be a
representative sample of what is on the market, and the manufacturers may change
their products or specifications without my knowing about it.
(1) What's the best scientific calculator to buy, and where's the best place
to buy one.
I prefer not to make
specific recommendations about manufacturers and vendors on this website, but I'll tell you what to
look for and where you can find some good prices.
First of all, don't buy one of those
six- or eight-function calculators that are little more than an adding machine.
Definitely do buy one with a two-line display, and I like very much algebraic
entry. (That's called V-S.P.A. M and EOS in TIs.) The two-line displays keep both your entry
and your answer on the screen at the same time. Make sure it has "Replay"
or some such provision for moving the cursor so that you can make
corrections. You'll also need an INS, insert, for entering things you may
have left out in your entry. Make sure it has a fraction function. That
looks like this: ab/c. It should
have provisions for entering powers of 10. That would be something like EE or
EXP. It should also have these: Trig functions, log, e^{x} ,
ln, nPr, nCr, and x^{2}, square root, and provisions for taking
roots and powers other than two (either x^{y} or ^.). Some
students may want complex number capability.
If you're attending an electronics technical school,
you might look for a calculator with BIN, HEX, and OCT. Some calculators have the
logic functions AND, OR, and XOR. Again these might be of some use to
electronic technicians or those aspiring to be. You can also evaluate a
logic expression such as ~(p.~q). But I've found that most teacher don't
use a calculator for evaluating logic functions, and most students don't go to the trouble to learn
how to use a calculator for that.
Where to buy: I'm
not going to tell you where to buy a calculator; I'm going to tell you some places they're
available. Wal-Mart, Best Buys, Office Depot, Office Max, Target (I
believe Target still has them.), and others that may be specific to your area.
You can buy a scientific calculator that is satisfactory for many people
students can be had for a little less than ten dollars. A Casio fx-300MS
sells for $9.73. A TI-30xIIs that is has a few more functions than the
Casio mentioned, sells for $14.96. A Casio fx115MS sells for $14.66.
This calculator has all of the normal functions mentioned above as being
necessary plus complex numbers and numerical integration and differentiation. These prices are as of 3/20/05.
=================
(2) How do you do fractions on a scientific calculator?
For most scientific calculator you use the
ab/c key. Let's say you wanted to add
1/3 + 1/4; then the keystrokes would be these: (Where the commas are for
separation only and are not entered.)
1, ab/c, 3,+, 1,ab/c,4,
=
=================
(3) How do you do mixed numbers on a scientific
calculator?
Read number 2 above and you can probably
figure it out yourself. Just put another ab/c
key stroke between the whole number and the fraction. Say you wanted
to add 4 1/3 + 3 1/4; then the keystrokes would be these. 4, ab/c, 1, ab/c, 3,
+, 3, ab/c, 1,
ab/c, 3, =. Your answer would be
7 7/12.
==================
(4) My calculator has second power and third power, but
how do you raise to a higher power such as 6?
The sequence of the
keystrokes may vary with the calculator, but the basic method is to use either the x^{y}
key or the ^symbol. Let's say you want to raise 6 to the sixth power; then the keystrokes
would be these: 6, x^{y} , 6, =. Note that if you press 2nd
or SHIFT, depending on the calculator, you can also use that same key to do
higher roots. For those calculators that use the ^ symbol, the keystrokes
would be 6^6=.
================
(5) I know what the EXP on my calculator is, but what's
the ENG for? That's for engineering units. These are usually expressed
in exponents that are multiples of 3. For example if you had 30000 on your
display and you pressed ENG, you'd get 30. 03. Meaning 30 x 10^{3}
. Similarly, .00001 would be displayed as 10. ^{-}06 .
==================
(6) What's the x^{-1} on my calculator for?
That will give you the inverse of a number. For example, 4, x^{-1}
will give you 0.25. On most scientific calculators you can convert that to
a fraction, 1/4, by pressing ab/c.
=================
(7) How do I change base of logs on a calculator? Calculators
only have two bases: log which is actually log_{10} and ln which is log_{e}.
If you want to do a log to some other base, divide the log by the log of the
base you want the answer in. (If you're using ln; then divide the ln
expression by the ln of the base.) Example: Find log_{7} 12.
On your calculator enter this: log 12/log 7. If you're not
sure if you did it right, you can always check it with these keystrokes:
<7>,<x^{y}>,<Ans> if your calculator has an Ans key.
------------------------
(8) I often get the wrong answer when I enter an expression with
several operations. Why?
You have to be careful to realize that the calculator will follow its order
of operations unless you tell it to do otherwise with grouping symbols.
Example:
2x3+ 4^{2}
2
This must be entered as follows:
(2x3 +4^{2})÷2
That'll give you 11.
If you enter 2x3 +4^{2}÷2, then
the calculator will first square 4 to get 16; then multiply 2x3; then divide 16
by 2 to get 8; then add 6 + 8 to get 14.
--------------------------
(9) What's the reason for parentheses on my calculator?
Well, I don't want to be dogmatic and say what the reason is, but
certainly an important reason is to give priority in the order of certain
operations. For example if we enter 16- 8÷4,
we'll get 16-2 = 14. If what we really wanted was to do the subtraction
first, then we can do that by writing this: (16-8)÷4. That'll give us 2.
Item 8, above, also deals with use of parentheses.
---------------------------
(10) How do I find what the angle whose cos is
0.5?
First make sure that your calculator is set
for radians or degrees, whichever you want the answer in. (Usually you'll want
it in degrees.) Most scientific calculators have the inverse trigonometric
functions as a 2nd or SHIFT function of the regular function keys. For
example, to find cos^{-1} 0.5, just press 2nd or SHIFT, whichever
your calculator has; press the COS button; then enter the argument 0.5 and press
= or ENTER or whatever your calculator has for executing an operation.
------------------------------
(11) I see the letters AOS and
EOS on calculator sheets. What do they mean?
AOS stands for Algebraic Operating System, meaning that it does the
arithmetic using the order of operations. EOS stands for Equation Operating
System, meaning that you make the entries just as you would write them in an
equation.
__________________
(12) What are the parentheses for on a Casio Scientific calculator?
Generally, parentheses on scientific calculators are used to change the
order of operations or to clarify the order of operations. All calculators do
not respond in exactly in the same way, but these examples will give you some
ideas about when you should consider parentheses. My advice to students is,
when in doubt, use parentheses. .
Ex 1: 3*5+3 = 18, but 3*(5+3) = 24
Ex 2: 20 + 4 + 8/2 = 28, but 20 + (4+8)/2 = 26
Ex 3: e ^{2} + 3 = 10.389, but e^{(2+3)} = 148.41
Ex 4: log 100 + 3 = 5, but log ( 100 +3) = 2.01
Ex 5: log 100 + 10² = 102, but log (100 + 10)² = 4.08
Be careful of this last one. On some calculators, for example the TI-83 Plus,
the expression log (100 + 10)² is treated as squaring the result of the
operation. You'll get 4.16 for an answer. To square only the argument on that
calculator, you'll need to enter this: log ((100 + 10)²). When you're uncertain,
the safe thing to do is to try a simple problem and see if you get the right answer.
---------------------------------------
(13) When I enter (-32)^(1/5); then (-2)^3 I get a correct answer,
-8, but when I enter (-32)^(3/5) I get Ma ERROR. Why?
It's probably because of the algorithm used in the last case. Evaluating
negative numbers with fractional exponents is a rather subtle issue, but the
subtleties arise out of some decisions about efficiency or cost that engineers
have make in the design or implementation. Your problem arises because early
designers of calculators chose to take advantage of the good algorithms for
natural logs that they already had and apply those to fractional exponents.
Here's how it went:
Solve the following:
y = x^{(3/5)}
ln y = ln x^{(3/5)}
ln y = (3/5)ln(x)
y = e^{((3/5)ln(x))}
Then they can use the log algorithm that they already have implemented in
hardware (originally) or software (later).
But it's clear that the last equation does not have the same domain as the first
one. The last equation becomes imaginary when "x" is negative. The first one
only becomes imaginary when x is negative and the numerator is odd and the
denominator is even.
Most scientific calculators, the TI-82 and the CFX-9850, do x^^{m/n}
using that logarithmic algorithm. Some of these calculators call that
problem a math error, others a domain error. The TI-83 Plus will handle
that expression okay. However, it has another subtlety: Some people think (-1)^{2/2} should
be +1, but the TI-83 Plus evaluates it as -1. That comes about when you
consider (√-1)^{2} . That just
removes the square root and leaves -1. I happen to agree with the way TI
does it, but I've done probably more than enough hand waving and I won't go into
that.
__________________
(14) My brother gave me an expensive calculator, HP-42S, without a book. I
can't even add on it. Can you help?
As it happens, a student of mine had an HP-42S and I spent a few minutes
figuring out how to use it so I could help her. So, I'll can give you some help
with the basics, but, sorry, I didn't get into the programming.
First of all, let's look at some of the functional keys.
1) Red key: The red key is pressed to shift the function of an
entry key to the red function printed on the panel above an entry key.
2) Menus: Notice that when certain functions such as MODES, DISP,
MATRIX and other such selections are made, the top row of entry keys is used for
selecting a menu item.
3) EXIT: The exit key is used to get out of the menu listing or other
non-standard entries.
4) MODES: The modes key is used to select the type of display such as
Degrees, Radians, Rectangular, and polar. Press the Red key; then the MODES
key. The top row of entry keys then becomes functional keys that correspond to
the menu on the bottom line of the display.
5) The DISP key is used for
selecting the number type of display such as Scientific, Engineering, and
Fixed.
6) Clear Key: The clear key, the large left-pointing arrow is used to
clear the X-entry. You can use the Red function of that key to clear other
entries.
A Few Words About RPN (Reverse Polish
Notation): HP calculator gurus swear by RPN, but most
of us prefer the regular algebraic --some of us even to the hybrid type that has
a few RPN and the rest algebraic. Anyway, one of its features is that you don't
use parentheses. Basically, you tell the calculator what mathematical operation
you're going to perform AFTER you enter the numbers. Let's go right to doing
some arithmetic.
Doing a Few Problems of Different Types:
1) 4 + 2: Press the following keys: 4, ENTER, 2, +.
You'll see the answer beside X.
2) 3 x 5: 3, ENTER, 5, x. Notice that ENTER is NOT pressed
after the last
number.
3) (7 + 5) ÷ (2 + 4): 7,
ENTER, 5, +, 2, ENTER, 4, +, ÷
. You'll notice that you enter divide in the last step. 4) 4^{2} :
4, ENTER, Red, x^{2} . You can use this same procedure of entering a
number and then the function with many of the keys, including these: 1/x, √x,
LOG, LN, 10^{x} , e^{x} .
5) 2^{5} : 2, ENTER, 5, y^{x} .
6) √(-9) : 3,+/-, ENTER, √x . Notice that the answer is given as a complex
number in rectangular form.
7) 6! (6 factorial): 6, ENTER, Red, PROB, N!
8) 6P3 (Permutations of 6 things taken 3 at a time): 6, ENTER, 3, Red, PROB ,
COMB. Other statistics are done in a similar way.
9) i^{98} : 1, Red, Complex, ENTER, 99, y^{x} . There may be
better ways of doing this.
10) Determinant of a 2 x 2 Matrix 1 ,2, 3 ,4: Enter the dimension: 2,
ENTER, 2, ENTER. Red, MATRIX, NEW. Enter data: 1, ENTER, XEQ (This is really
the --> key), 2, ENTER, XEQ, 3, ENTER, XEQ, 4 ENTER, DET. There may be other
ways to do this, but this will work for any matrix.
This is the basics. There are many other
functions which should be become obvious if you understand the method in these.
------------------------------------
(15) What does S-V.P.A.M. on the Casio scientific calculator s mean?
It's for sure you'll never find that information in the user
manuals. Actually, it stands for Super Visually Perfect Algebraic Method.
The Algebraic Method part applies to the idea that you can enter an expression
the way you would write it down. For example, if you wanted to find the
sine of a 45 degree angle on some other scientific calculators, you would enter
[9],[0], [sin],[=]. On the S-PAM you would enter [sin], [9],[0], [=], the
way you would write it down. The visually perfect allows you to have the
entry and the answer both displayed at the same time. Incidentally, this
isn't just hype. Both of those features are very useful features in my
opinion. The PAM for the Casio is about the same as EOS for the TI, if
that means anything to you. (See Item 11 above.)
___________________________
(16) Will the Casio fx-7400G do fractions?
I think not. Here's a short program you can enter if you have enough
memory left. It takes about 90 bytes of memory. There are, no doubt,
better programs, but this is a quick and dirty one that works.
Ans->A: 0->K:1->D:0->N
Lbl 1
N+1->N
Lbl 2
K+1->K
D+1->D
K>999=> Goto 3 (=>is not greater than or equal to, but the
symbol gotten by SHIFT, 7.)
N÷D-A->T
T>.000001=>Goto2
:T<0=>Goto 1
Lbl 3
N▲
(▲ is the symbol gotten by SHIFT, :)
"÷":D
Notes:
1. The formatting leaves something to be desired, but it works after a
fashion. When -Disp- appears at
the end of the program, press EXE to get the total
answer.
2. You must use the program immediately after you do the fraction
operation so that the correct answer
will still be in the Ans location.
3. With large numerators and denominators, the calculation takes quite
some time, perhaps up to 30 or
40 seconds. But with small ones it's reasonably
fast.
4. You could change the number is the K> step to 99 if you want to
limit the capability to smaller
fractions.
5. If there is no fractional equivalent, the program does not return the
decimal, but gives you an
incorrect answer. I did not want to use very scarce memory to
do that, but you could add those
steps if you want to use the memory.
Last Revised: 10/17/05