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I have a calculator that I found recently that has a base 5 option. It has options labelled HEX, BIN, DEC, OCT, and PEN. My son set it on PEN, and no numbers above 4 worked anymore. Playing around with it, it was clearly base 5. (E.g. 22 divided by 3 is 4).

Why does any calculator have base 5? The other bases are commonly used in computer science, but I can't think of the slightest reason why anyone would need base 5 on a calculator.

The calculator is by Sharp, with the number EL-W535 and the word Writeview.

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Doesn't the abacus use base-5? – Fred Kline Jan 19 '14 at 2:22
The Mayans used a modified base system that involved 5 and 20. Fingers 'n' toes. – ncmathsadist Jan 19 '14 at 2:24
The mayans wore sandals or went barefoot.… – ncmathsadist Jan 19 '14 at 2:26
The japanese abacus uses base 5 as a sub-base for base 10. We could say it's hybrid between the two, but in fact it's much more near base 10. An interesting fact is that learning to calculate with an abacus is supposed to help with mental calculation, since the brain associates the calculations with movements and an image of the abacus. – Olivier Jan 19 '14 at 2:34
I am wearing flip-flops, but I can't use my toes for counting because they are so gnarly they would be considered transcendental numbers. – Fred Kline Jan 19 '14 at 2:45

Apparently, some computers in the 50's used a system to describe the decimal system which had base five digits, and another bit to represent if it was between $0-4$ or between $5-9$, known as a biquinary system.

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Base 10 is used because humans have 10 fingers. The base 5 could be the result of some inside joke or interest by a Sharp engineer. You can do base 5 arithmetic with one hand and count pretty high using two hands. Two-handed arithmetic in base 5 could be interesting, especially multiplication. But I can only guess.

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There are some cultures such as Gumatj that used base 5 with 25 the next level up.

Though I have to think that the real reason is the programmers for the calculator were playing an inside joke.

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