Is there a fancy name for the "left side" and "right side" of a decimal number?
(That is, the pre-decimal part and the post-decimal part.)
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The integer part, or integral part of a decimal number is the part to the left of the decimal separator. (See also truncation.) The part from the decimal separator to the right is the fractional part.
In normal use, "integer part" and "fractional part" does reign supreme.
However if the decimal is used in the context of logarithms, the terms you want are "characteristic" and "mantissa". A generation ago, when sliderules were common, these terms were better known.