def find_pi_to(accuracy):
    i = 1
    approx = 4.0
    while 1:
        term = (2 * i) + 1
        if i % 2 == 1:
            term = -term
        new = approx + 4.0/term
        if abs(new - approx) < accuracy:
            approx = new
            break
        i += 1
        approx = new
    return approx