Sunday, March 14, 2021

[dzjudglx] rounding to enable further rounding

when rounding a number, provide extra digits to avoid a rounded result ending in 5 or 50 or 500 ...

for example, avoid rounding 123.45032 to 123.450 or 123.45; instead, round it to at most 123.4503 (or all the way to 123).  this is so that if the reader should wish to round further, it's clear whether to round up or down.  that is, should an already rounded number 123.450 be rounded to 123.4 or 123.5 if only one digit past the decimal point is desired?  the original number could have been anywhere between 123.4495 and 123.4505.  some of that range should be rounded down to 123.4, some up to 123.5 .

demonstrated on some previous posts: decimal approximation of roots, Riemann zeta zeros.  these were easy cases because the underlying numbers could be calculated to arbitrary precision.  i don't know what to do regarding significant figures of a physical measurement.

previously, is the sublimation temperature of dry ice closer to -79 C or -78 C?

to do: computer program to perform this kind of rounding.

perhaps if a rounded result ends in 5, 50, etc., append a superscript plus or minus to indicate whether the result before rounding was greater or less than the rounded result.  but this could be confusing if the value itself is negative.  use a third symbol to denote exactly equal to 5, 50, etc.

maybe this problem goes away if, instead of base 10, we used an odd base.  but does the problem occur in balanced ternary?

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