import math


def around(number, digitCount=3):
    """
    Rounds a number to the first `digitCount` digits after the appearance of
    the first non-zero digit ("adaptive round").

    >>> around(1234.56789, 3)
    1230.0

    >>> around(0.00123456789, 3)
    0.00123
    """

    try:
        magnitude = math.floor(math.log10(abs(number)))
    except ValueError:
        magnitude = 0
    roundDigitCount = int(digitCount - magnitude - 1)
    return round(number, roundDigitCount)