This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.

ExponentFunction

ExponentFunction is an option for NumberForm and related functions which determines the exponent to use in printing approximate real numbers.

Functions like NumberForm first find the exponent that would make exactly one digit appear to the left of the decimal point when the number is printed in scientific notation. Then they take this exponent and apply the function specified by ExponentFunction to it. If the value obtained from this function is an integer, it is used as the exponent of the number. If it is Null, then the number is printed not in scientific notation.

The argument provided for the function specified by ExponentFunction is always an integer.

In NumberForm, the default setting for ExponentFunction never modifies the exponent, but returns Null for machine numbers with exponents between and 5, and for high-precision numbers where insignificant zeros would have to be inserted if the number were not printed in scientific notation.

In ScientificForm, the default setting for ExponentFunction never returns Null.

In EngineeringForm, the default setting for ExponentFunction returns an exponent that is a multiple of 3.

In AccountingForm, the default setting for ExponentFunction always returns Null.

See The Mathematica Book: Section 2.8.7.