HP 41 number display



let me say first that I have been using mostly TI and later Casio calculators as I could not afford an HP at school in the late '70s / early 80's. Now I am trying to get familiar with HP 41 emulators on my PalmOS device and on PC (Windows/Linux) as those are the best programmables available and out of historic interest.

The TI and Casio calculators when running in standard display mode (default), always use a variable size display of number, so e.g. the number 0.125 displays as 0.125 and 0.3 displays as 0.3 etc. - with the number of fraction digits as needed. This kind of display fits my needs best.

However I could not find a way to get the HP-41 into this kind of display mode - it appears the number of digits after the decimal point is always fixed and it starts up with 4 (I am aware how this can be changed to other fixed sizes).


Am I overlooking something?

Is there a way to get variable digit display with the HP-41 and if yes, how can it be set up?

Thanks for any hints.



Edited: 12 Nov 2005, 2:34 p.m.


Hello Gileno,

Sorry, there is no floating point display available on the Hp-41 and most Hps by the way...

Why not try the Hp-35 ;-)

Best regards



Hello Etienne,

Hello Gileno,

Sorry, there is no floating point display available on the Hp-41 and most Hps by the way...

Why not try the Hp-35 ;-)

by the way, my name is Guido, not Gileno ;-)

Thanks for your response and sorry to hear this functionality is not available with the HP 41 although I thought it was pretty standard.

May I ask how you deal with the fact that this is not available?

Do you frequently change the fixed number of digits to maximum and back when you see that the last digit displayed is not zero after a calculation?

Or do you simply go with the rounded version?

I have a bad feeling when leaving the setting at maximum fixed digits because then its hard to recognize due to the possibly high number of zeroes.

(It's however clear to me that even if not everything of a number is displayed, it will still internally be used for the following calculations).




Hello Guido,

I just set the the display to the disered number of decimal places and carry on. Any fractional part of a calculation that falls outside the display format is insignificant anyway. That said, however, I sometimes do set to 9 decimal places and back just to have a look...it's 6 keystrokes and really no big deal.

Best Regards, Hal


Hello Guido!

I apologize for the name change (I was alsobtrying to post to another member named Gileno).

Many fellow members have already responded inb this thread about useability of the digit.

For myself, and even if I like Hps, I definitely miss the floating point because fixed decimal is NOT the way I write numbers on the paper myself or even pronounce them when I talk :

- at work, I deal with financial amounts, so Fix 2 is fine, no problem to use nearly all my Hp calcs.
- at home, when I want simplicity, I use an Hp-35, an Hp-71B, an SR-50 or SR-51.

I just can't explain to my 8-years old daughter that 5 x 6 = 30,000

and I certainly won't...

Best regards from France!



Newer HPs have an additional display mode, ALL, which suits your preference. But HP41 hasn't it.

Usually you just choose the number of digits appropriate for your current task, and answers will be so formatted. Internal representation, as you said, is always kept at maximum precision. Once you get familiar with this usage, you like it very much.

Non-zero values will never be shown as zero. In such particular case the display temporarily switches to SCIentific notation and will show something like 1.0000 -05 (instead of 0.0000).

Best regards


I won't presume to tell you whether or not the least significant parts of the mantissa are important for the work that you are doing. I will suggest that you can view those least significant digits in the HP-41 in the same way that you viewed the so-called "guard digits" in the TI and Casio machines. Some examples follow. Start with the calculator in Fix 9.

Playing with pi:

1. Place the value of pi in the display; i.e. the ten digit value 3.141592654

2. Divide pi by 4 and see 0.785398164 in the display but you know that the pi value in step 1 divided by 4 should be 0.7853981635 .

3. To see all ten digits of the mantissa simply multiply the displayed value (x register contents) by ten and see 0.7853981635

4. Place pi in the display and see 3.141592654

5. Square the displayed value and see 9.869604404

6. Square the displayed value again and see 97.40909109

7. Take the reciprocal of the displayed value and see 0.010265982; i.e., ten digts but only eight digits of the mantissa.

8. Multiply by 100 and see 1.026598225; i.e., all ten digits of te mantissa.

By now you should be able to see that what was done to see the least significant digits of the mantissa is the same kind of thing that you do with TI and Casio machines to see the guard digits.

Some trigonometry in DEG mode:

1. Enter 45, press sin and see 0.707106781 in the display.

2. Multiply by ten and see 7.071067812; i.e., all ten digits of the mantissa in the display.

3. Again, enter 45, press sin and see 0.707106781 in the display.

4. Enter 45, press cos and see 0.707106781 in the display.

5. Subtract and see 0.000000000 in the display.

Some trigonometry in RAD mode:

1. Enter pi, divide by 4, press sin and see 0.707106781 in the display.

2. Enter pi, divide by 4, press cos and see 0.707106781 in the display.

3. Subtract and see 2.0000000- 10 in the display.

To understand the result in step 3 above:

1. Enter pi, divide by 4, press sin and multiply by ten to see 7.071067813; i.e., all ten digits of the mantissa of the sine of pi/4.

2. Enter pi, divide by 4, press cos and multiply by ten to see 7.07106811; i.e., all ten digits of the mantissa of the cosine of pi/4.

3. Note that the two mantissas are different by two in the least significant place.

4. Why are the sine and cosine of pi/4 slightly different? Because the actual value of pi/4 is 0.78539816339... while the value of pi/4 in the HP-41 is 0.7853981635 slightly higher than the exact value. The sine of an angle slightly higher than pi/4 should yield a value slightly higher than the sine of pi/4. The cosine of an angle slightly higher than pi/4 should yield a value slightly lower than the cosine of pi/4. You can do the arithmetic.


One of the things in my startup routine (automatically executed when I turn the 41 on) is to put the calc in ENG 3 since that's what I usually use. Rarely I'll do ENG 6, and even more rarely, need to view the final digits in something right near 1 (like 1.000000042), so I'll just subtract 1 to see what's out there. My HP71 has STD which is the type of display you're asking about, but I've never missed it on the 41 at all.


I'd have to say that the 41 does it right, as do most of the older HP calcs. I vividly remember one of my university tutors marking me down on a problem for providing more significant digits in the answer than the problem - and the measurement technology implicit in it - warranted.

When I acquired my HP-45 a few months later, I was pleased to notice that it defaulted to FIX 2, although with large values, even that provides the unsophisticated novice with an unjustifiable impression of accuracy.

Lots of digits is something mathematicians might like - but engineers should know better.



--- Les



I have no problem with the idea that some engineering disciplines do not need the full ten digits available from the HP-41. Some do; e.g, inertial navigation, which was my field of engineering from 1960 through 1990.

The issue of how many digits are enough is not a new one. Back in the early 1980's much of my analysis software was in BASIC on a company-owned time-share computer. A friend suggested that I transfer my programs to an Apple computer since the company was providing Apples as desk-top computers. I converted a program but it wouldn't run my test case satisfactorily. Another friend suggested that I should use Microsoft BASIC rather than Applesoft BASIC. When I did that I got resonable answers to my test case. About that time in the June 1982 issue of Call Apple a user asked the Apple Doctor ""I wonder if you could explain why the Apple languages Applesoft, Pascal and Fortran have used only 32-bit floating point numbers which will give only six-seven place accuracy. Microsoft Basic-80 and Fortran used with the Z-80 Softcard offer the additional double precision numbers with 64 bits. ..." Part of the answer in defense of of lesser numerical precision of the Apple software said "It is derned difficult to measure something to nine significant figures ..."

I didn't move away from the time-share computer even though it was S - L - O - W and it was inconvenient to go to the terminal rather than work at my desk. What it offered was an extended BASIC including double precision calculations, matrix arithmetic including calculation of determinants, inverses, transposes, scalar products, vector products, and the like. I had started using the time-share computer in 1967 and was using it regularly when the HP-35, HP-45, HP-65 and HP-67 came on the market. I had no use for any of those devices. They simply didn't offer the calculating power that I had become used to. The TI-59 was the first hand-held capable of doing the work that I needed.


I have no problem with the idea that some engineering disciplines do not need the full ten digits available from the HP-41. Some do; e.g, inertial navigation, which was my field of engineering from 1960 through 1990.

Funny you should mention that, Palmer - I'm currently reading "Feynman's Tips on Physics" (the missing lectures from the Lectures books), in which Chapter 4 (Review Lecture D) is on the topic of "Dynamical Effects and their Applications", covering gyroscopes and accelerometers, and their application to inertial navigation, which was very new in the early sixties. The end of the chapter is a transcript of Feynman's conversation with students as they examine a gyroscope (his mike was left open and the tape recorder running).

As a pilot myself, I've had exposure to the principles; I can still remember learning how a laser ring gyro works and being amazed that we can use light travelling around a fiber in that way.

So I agree with you about the need for precision in some applications, and of course, we need to preserve that precision through intermediate calculations. We also need to understand numerical methods, so we know when precision is being lost. But all in all, I like being able to set the display to round to two digits after the point as a reminder that all the digits I'm not seeing are generally not justified.


--- Les



As I see it the obvious use for fix 2 is in financial calculations, where in other modes the extra zeroes are annoying.

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