import random

def random_around_zero(r):
    """ 
    Return a random float in the range [-r, r]
    """
    width = 2 * r
    return random.random() * width - r

def random_throw(r):
    """
    Return a random point in the square 
    [(-r, r), (r, r), (r, -r), (-r, -r)]
    """
    x = random_around_zero(r)
    y = random_around_zero(r)
    return x, y

def in_circle(r, x, y):
    """
    Return True if (x, y) is in a circle with radius r 
    centered at 0. Otherwise False.
    """
    distance_from_center = (x * x + y * y) ** 0.5
    return distance_from_center <= r

def number_in_circle(n_total, r=0.5):
    """
    Test n_total random points (x, y) in a square with 
    sides 2r and return the number of points that are 
    inside a circle of radius r.
    """
    n_circle = 0
    for i in xrange(n_total):
        x, y = random_throw(r)
        if in_circle(r, x, y):
            n_circle += 1

    return n_circle

def main():
    for i in range(9):
        n_total = 10 ** i
        n_circle = number_in_circle(n_total)
        pi = 4.0 * n_circle / n_total
        print '1x10^' + str(i) + ':', pi


if __name__ == '__main__':
    main()