What are the two 'sides' of a decimal number called?

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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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We really do use "integer part" and "fractional part" respectively: see Wikipedia, e.g., on decimal fractions.

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.

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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.