In the ideal situation, I think you are better off changing it to decimal, change the scale to nano (x 10-9), and get rid of the exponential part. e.g. 1.23456E-8 Units ==> 12.3456 nanoUnits. Since you want a format like 12.23, you would change the field to decimal(4, 2), and enforce your 2-digit mantissa (scale) rule automatically (with automatic rounding to a 2-digit mantissa.)
Since users might be confused at first by the change of units, you could convert from native Units to nano-Units in the client app.