def decimal_to_binary(v: float, precison: int = 6) -> str:
    if v == 0:
        return '0b0'

    binary = ''
    integral = int(v)  # integral part
    mantissa = v - integral  # fractional part

    # conversion of integral part to binary equivalent
    # quotient, modulus = divmod(integral, 2)
    # while quotient:
    #     binary += str(modulus)
    #     quotient, modulus = divmod(quotient, 2)
    # binary += str(modulus)
    while integral:
        binary += str(integral % 2)
        integral //= 2

    binary = binary[::-1] + '.'

    # conversion of fractional part to binary equaivalent
    while precison > 0:
        precison -= 1
        mantissa *= 2
        if mantissa == 1:
            binary += '1'
            rpartition = binary.rpartition('.')
            return '0b' + rpartition[0] + '.' + rpartition[2].ljust(precison, '0')
        elif mantissa > 1:
            binary += '1'
            mantissa -= 1
        else:
            binary += '0'

    return '0b' + binary


print(decimal_to_binary(13.7))
print(decimal_to_binary(8.1))
print(decimal_to_binary(.1))
print(decimal_to_binary(4.))
print(decimal_to_binary(4.5))