Modern, lets say, post turn of the century popular languages all support some kind of rational data type allowing native fraction arithmetic. https://en.wikipe

Modern, lets say, post turn of the century popular languages all support some kind of rational data type allowing native fraction arithmetic. https://en.wikipedia.org/wiki/Rational_data_type https://en.wikipedia.org/wiki/Rational_data_type Anyway... It turns out that humans like numbers that are evenly spaced like 1/10, 2/10 (1/5), 3/10, 4/10. That all seems pretty evenly spaced to us, but its actually totally arbitrary that we have 10 handy (ugh the puns) appendages. If we chill with space aliens they will think numbers are evenly spaced like 1/14, 2/14 (aka 1/7), 3/14, 4/14 (aka 2/7)... much like jamming a metric socket on an imperial nut to fix your car, the amount of error varies wildly base on size. You can get away with a 9/16 socket on a 10 mm nut most times, but a 15/16th socket will probably require a hammer to fit a 24mm nut. Or just round off all the nuts with a vise-grip pliers. Anyway the space alien's 7/14 is actually a perfect match to our 5/10 but the amount of error varies from not much, to quite a bit, in the other attempts at interplanetary standardization. Likewise if you think of the computer as a space alien (not too far from truth, I sometimes feel) it uses binary and thinks numbers like 1/8, 2/8 (1/4), 3/8, are evenly spaced. Or as some specific example expressing our 1/2 in floating point is pretty easy for most computers while expressing 1/5 or 1/3 is somewhat less successful, or somewhat far in error compared to our closest 1/10th based numbers. In the old days like half a century ago there were competing software floating point designs with varying levels of success vs speed. Everything is super boring today and standardized. 72 bit pdp-10 floating point was from a romantic adventurous era, like an Indiana Jones movie (well, one of the good ones). IEEE 754 is modern and better in all regards, yet has all the panache and style of a modern econobox commuter car. Think of the glory of PDP8 Fortran floating point spread unevenly across three words of four octal digits, 2 bits of signs, 2 bits MSB of mantissa, and 8 bits of exponent in the first 12 bit octal word, now that is something glorious to wake up to in the morning.