Arithmetic
Key in the first number, press ENTER, key in the second number, and then press the button to subtract, add, multiply or divide.
2 Enter 3 + (5.00)
If the first number is already in the display, just key in the second number, and then press the desired button.
4 x (20.00)
See Reverse Polish Notation for how all that works.
Trignometric Functions
The SIN, COS and TAN buttons calculate sines, cosines and tangents. You key in an angle and press the button to get the relevant result.
Pressing the blue function button first gives access to SIN-1, COS-1 and TAN-1. These calculate the reverse: the angle whose sine, cosine or tangent is the value you keyed in or which is already in the display.
An example:
4 5 SIN (0.71) [blue] SIN-1 (45.00)
The calculator has a DEG-RAD switch on the right hand side, under the display. This sets the "angle mode" to "Degrees" or "Radians".
A full circle is 360 degrees so 90 degrees is a turn of a quarter of a circle or two lines at right angles to each other. An eighth of a circle is 45 degrees and so on.
The circumference of a circle is 2 * pi * the radius. A one meter circle has a circumference of 6.28 meters. If you went a quarter of the way around the circle, you would have gone 1.57 meters. "Radians" are how far around a standard size circle you go. A standard size circle has a radius of 1. This can be 1 meter, 1 foot, 1 mile or 1 lightyear .... It's all proportional so it always works for any unit of measure.
Converting between degrees and radians is fairly straight forward after you get used to them. The thing to remember is 360 degrees is the same as 2 * pi (6.28) around a "unit" (radius=1) circle. So: 180 degrees = 3.14 radians, 90 degrees = 1.57 radians, 45 degrees = 0.78 radians and so on.
If you need to calculate a trignometric function of something in radians
then just: flick the switch to RAD, key in the radian value, and press the
SIN, COS or TAN button. eg:
[RAD] 3 . 1 4 COS (-1.00)
You can use the DEG-RAD switch to convert between degrees and radians. This
works for angles between 0 and 180 degrees (radians 0 - 3.14):
[DEG] 4 5 COS (0.71) [RAD] [blue] COS-1 (0.78)
It only works for 0-180 degrees because angles over 180 degrees have the
same cosines as angles below 180 degrees.
When in doubt:
Divide radians by 2 pi and multiply by 360 to get degrees, and
Divide degrees by 360 and multiply by 2 pi to get radians.
Those always work.
More Functions
| 1/x | This calculates one divided by the displayed value. eg: 5 1/x (0.20) |
| ex | "e" (2.72) raised to the power "x" (the value in the
display. eg: 2 ex (7.39) |
| CHS | CHange Sign. x -> -x. eg: 5 CHS (-5) |
| yx | "y" raised to the power of "x". eg: 3 ENTER 2 [blue] yx (9.00). |
| LN | Natural logarithm. The opposite of ex. What number must
we raise e to, in order to get the value in the display.
eg: 7 . 3 9 [blue] LN (2.00) |
| LOG | Log to the base 10. What number must we raise 10 to, in
order to get the value in the display. eg: 1 0 0 0 [blue] LOG (3.00) |
| 10x | Raise 10 to the power "x" (the value in the display). eg: 3 [blue] 10x (1000.00) |
| /x | Square Root of "x" (the value in the display). eg: 9 [blue] /x (3.00) |
| PI | Pi. eg: [blue] PI (3.14) |
Stack Functions
| X<->Y | Exchange "x" and "y". This swaps the value in the
display and the prior answer. eg: 5 ENTER 2 / (2.50) 3 X<->Y (2.50) - (0.50) |
| Rv | Roll Down. This moves the stack values "down". "t" goes
to "z", "z" to "y", and "y" to "x". The old "x" value
is now in the "t" register. See The Stack for more details. eg: 1 ENTER 2 ENTER 3 ENTER 4 Rv (3.00) Rv (2.00) Rv (1.00) Rv (4.00) |
| CLx | Clear x. This removes the value currently in the "x"
register (the display). It looks like it has been set to
zero, which it has, but it also means anything keyed in
will replace the zero - without lifting the stack. eg1: 2 ENTER 3 CLx (0.00) 4 + (6.00) eg2: 2 ENTER 3 CLx (0.00) + (2.00) |
| CLR | Clear Registers. This clears the entire stack. "x", "y",
"z" and "t" all become zero. eg: [blue] CLR (0.00) |
The ENTER key is also a stack key (it copies what is in the "x' register into the "y" register, lifts all of the other stack values, and allows anything keyed in to replace the "x" (displayed) value.
Memory
| STO | Store. Saves the "x" value in a memory. |
| RCL | Recall. Gets the saved value back. Anything in the "x"
register is pushed up the stack. eg: 1 ENTER 2 STO + (3.00) RCL (2.00) + (5.00) |
| M+ | Memory Plus. Add the displayed value to what is in the
memory. eg: 4 STO 3 [blue] M+ (3.00) RCL (7.00) |
| M- | Memory Minus. Subtract the displayed value from what is in
memory. eg: 4 STO 3 [blue] M- (3.00) RCL (1.00) |
| M* | Memory Times. Multiply what is in memory by what is in the
display. eg: 4 STO 3 [blue] M* (3.00) RCL (12.00) |
| M/ | Memory Divide. Divide what is in memory by what is in the
display. eg: 4 STO 3 [blue] M/ (3.00) RCL (1.33) |
Scientific Display and Precision
In science, where numbers are often very large or very small, it is impractical to write values like 0.00000000000034 or 45127000000000. Instead "scientific notation" was created to express numbers with a certain "precision" and "magnitude".
The "precision" is "how precise" or "to how many decimal places". Pi is 3.14 to two decimal places. This is not as precise as specifying it to four decimal places, 3.1416, or to six decimal places, 3.141593. In engineering and science you often don't need to be really really precise. If you are making a chair with a height of 1 meter, it probably should end up between 0.99 meters and 1.01 meters high to be usable. If you are very focussed on quality you might make it within 0.999 meters and 1.001 meters ie accurate to a millimeter (pretty close). Getting it more accurate than that will be difficult without the use of special and expensive tools. Is anyone going to buy your chair if it cost $10,000 to make? Are you going to be able to make any more if you can't sell the first. There are trade-offs involved.
If you are a scientist measuring the distance to the star "Alpha Centauri", how accurately can you measure it? There is little point in spelling it out to the millimeter if your equipment isn't that accurate. And which part of Alpha Centari are you measuring the distance to? And from which part of Earth? From what floor of that building? The Earth moves around the Sun so the distance will depend on where we are in our orbit. And the universe is said to be expanding so, just after you publish, it will be too short.
Precision allows us to say the distance from here to Alpha Centauri is 4.2 light years and it doesn't matter which part of Earth, which part of Alpha Centauri, where we are in orbit, or how much the universe has expanded. The distance is still 4.2 light years.
"Magnitude" is "how big". In science, something 10 times bigger is often classed as "a magnitude" bigger. 1, 10, 100, 1000 are expressed as powers of 10 (as 0, 1, 2, 3). This makes 0.00000000000034 into 3.4x10^-13. 3.4 is an easy number to compare to something twice the size (6.8) or half the size (1.7). You don't have to worry about all the zeros - that is addressed by the magnitude bit - the x10^-13. The "-13" means there are thirteen zeros involved, and they are all to the left of the 3.4 decimal point. If it were "13" (without the minus) there would still be thirteen zeros involved - but they would be to the right of the decimal point.
Examples of scientific notation are:
3.4 x 10^-13 = 0.0000000000003.4
3.4 x 10^ 13 = 34,000,000,000,000
2.0 x 10^ 0 = 2.0
2.0 x 10^ 3 = 2000
2.0 x 10^ -3 = 0.002
| EEX | Enter EXponent. This allows you to key in a number in
scientific notation. eg1: 1 ENTER 2 EEX 3 ( 2 03) + (2001.00) eg2: 4 EEX 2 ( 4 02) CHS ( 4 -02) ENTER (0.04) 1 + (1.04) eg3: 2 EEX 3 ( 2 03) ENTER (2000.00) 4 EEX 2 ( 4 02) CHS ( 4 -02) * (80.00) |
| DSP | Display Precision. Follow this with a number from 0 to 9
to set scientific mode with 0 to 9 decimal places eg1: 200 DSP 0 ( 2 02) eg2: DSP 1 ( 2.0 02) eg3: DSP 2 ( 2.00 02) |
| DSP . | Display Precision. If you follow the DSP key with a
decimal point, the calculators goes into normal "fixed
point". Follow this with a number from 0 to 9
to set fixed point mode with 0 to 9 decimal places eg1: 200 DSP . 0 ( 200. ) eg2: DSP . 1 ( 200.0 ) eg3: DSP . 2 ( 200.00) |
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