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Has anyone encountered or used the pental (base 5) number system? I came across it by chance when I was playing around with my grandson's Sharp EL-531W scientific algebraic calculator, which we had just bought for him at the supermarket for $12.99, so it's pretty much a low end calculator similar to the HP SmartCalc 300s. I am familiar with binary, octal and hexadecimal numbers for use in programming and computer applications, but I have never before seen the use of pental numbers (e. g. 6 decimal = 11 pental). So, at the risk of appearing grossly ignorant, what would be the application for such a number system? I've never seen it on any of my HP calcs; even the mighty HP-50g lacks it.

Please help me before I lose face with my grandson, who thinks I am the eternal fountain of knowledge.


OK, so I see it has been discussed before, but no explanation as to its practical use. Perhaps it has some mystical or religious meaning as in a pentagram? Or maybe some insane programmer at Sharp just put it on their calculators to scare away evil spirits.

I'm going to guess it is something to do with the abacus.

Here's another Sharp pental calculator :-)

Some math textbooks for middle school kids have used base 5 to teach kids about other number bases, so they can better understand and appreciate our base 10 system. But I have never seen any teacher spend any time on this at all. Since base 10 is, supposedly, based on our 10 fingers, base 5 would represent one hands-worth, I guess. It has no practical value.

I don't know any machine using the pental number system, but I know one exemple of a ternary (base 3) computer:

Setun computer



Your photo of the hybrid calculator is awesome! At first I thought maybe you were pulling my leg, however, after doing some research I find that it is legitimate. Soroban

I'm going to guess it is something to do with the abacus.

Or more specifically, the Japanese version of the abacus. It makes sense that since Sharp is a Japanese company and that early Sharp calculators were manufactured in Japan, then they would incorporate the Japanese abacus into their calculators. I have seen old Japanese storekeepers still using the Japanese abacus, as I have seen Chinese using the Chinese abacus. Perhaps Sharp incorporated the pental number system into some of their more recent calculators to teach Japanese schoolchildren about the Japanese abacus.

Thanks for your contribution,


ternary was apparently quite popular. There's some trick you can do with -1, 0, 1 being your system.

but pental?

aren't roman numerals a bit pental. They appear to be based around changing the symbol at units of 5.


I think the correct word for a number system based on five is quinary.

Here is an interesting link :

The Quinary System

But as to why the calculator has it in these modern times, I have no idea ?


Your photo of the hybrid calculator is awesome!

It's actually from this very interesting site: