a b/c unexpected function

[Joe Horn]

A similar question was recently posted on HP's Calculator Forum. For your convenience, my reply there is copied below:

Joe Horn Wrote:When [a b/c] is pressed in Home view in Standard display mode, here's what is calculated:

First press = QPI(input, 10)
Second press = PDQ(input, 11)

QPI is a built-in function. See its Help screen for details of how it works. It tries to identify "recognizable" numbers, but its result should never be believed blindly. For example, it says that pi^2 is 208071/21082. That's only an approximation, not an exact result.

PDQ is the algorithm used by the second (and sometimes third) press. Its accuracy is controlled by the current display mode. For example, try Fixed 6 mode and see 0.000001 displayed as 1/500001 which seems absurd until you realize that reducing the display setting controls PDQ's accuracy. PDQ is only available via the [a b/c] key, but if you want to learn how it works and use it as a stand-alone program with user-settable accuracy, it is available HERE.

Disclaimer: Although HP incorporated my PDQ algorithm into the Prime's [a b/c] key, I do not work for HP. I'm just another happy HP calculator enthusiast.

In other words, the second press of [a b/c] in Home view is intended to give you the simplest fraction which falls in the interval of the displayed number plus or minus the accuracy of the current display mode. ("Simplest fraction" here means the ratio of two integers which are as small as possible.) It's important to know that both presses of [a b/c] return approximations, just using different algorithms which answer different questions.