Base π²

from math import pi, log, ceil, floor
base = pi ** 2
mode = input("[T]o base or [F]rom base? ")[0].upper()
while not mode in "TF":
    mode = input("[T]o base or [F]rom base? ")[0].upper()
if mode == "T":
    num = orig = float(input("Number: "))
    result = ""
    error = float(input("Maximum error %: ")) / 100
    if num < 0:
        result += "-"
        num = -num
    power = floor(log(num, base))
    if power < -1:
        result += "." + (-power - 1) * "0"
    while num > orig * error or power >= 0:
        mul = num // (base ** power)
        num -= mul * (base ** power)
        if power == -1:
            result += "."
        result += str(int(mul))
        power -= 1
    print(result)
    print("Error: %4.1f%%" % (100 * num / orig))
else:
    num = input("Number: ")
    error = float(input("Maximum error %: ")) / 100
    minus = False
    if num.startswith("-"):
        num = num[1:]
        minus = True
    result = 0
    power = len(num.split(".")[0]) - 1
    for c in num:
        if c == ".":
            continue
        result += int(c) * (base ** power)
        power -= 1
    if minus:
        result = -result
    digits = -len(str(result).split(".")[0])
    while abs(round(result, digits) - result) / result > error:
        digits += 1
    result = round(result, digits)
    print(result)