Base converter with fractions?

[Dieter]

(01-26-2017 05:18 PM)Joe Horn Wrote:  Unfortunately that amount of initial roundoff introduces a great amount of error.

Sure. The example rounds to four decimal places, so the result of course is not correct in all 12 digits, let alone the exact answer.

(01-26-2017 05:18 PM)Joe Horn Wrote:  Smith's BASECALC converts 3.142 (decimal) to "3.06646410512335" (base 7), which it converts cleanly back to what we started with, namely 3.142 (decimal),

FTR: this still is not the exact result, it's just the first 15 digits. The exact base-7 representation of 3,142 is periodic, it's \(3,\overline{06646410512335362252}\).

Since we're in a museum here: one of my first books on RPN and calculators included an HP67/97 program for base conversions, both for integer and fractional numbers. The method has been posted here: simply multiply the fractional part by the base, then the integer part of this is the next digit. I just noticed that this book is available on Google books (Helmut Alt, Anwendung programmierbarer Taschenrechner Band 1). If you read German: it's page 140ff.

Dieter