Calculate Period Length Of Recurring Decimal Fraction

I want to do a program in python (3.6.5) that tell the length of e.g. 1/7. The output should be for this example something like: 'length: 6, repeated numbers: 142857'. I got this s

Solution 1:

Doing print ("repeated numbers:", t) prints the representation of the t function itself, not its output.

Here's a repaired version of your code. I use a Python 3.6+ f-string to convert the repeating digits to a string, and add zeros to the front to make it the correct length.

deffind_period(n, d):
    z = x = n * 9
    k = 1while z % d:
        z = z * 10 + x
        k += 1

    digits = f"{z // d:0{k}}"return k, digits

# Test

num, den = 1, 7
period, digits = find_period(num, den)
print('num:', num, 'den:', den, 'period:', period, 'digits:', digits)

num, den = 1, 17
period, digits = find_period(num, den)
print('num:', num, 'den:', den, 'period:', period, 'digits:', digits)

output

num: 1 den: 7 period: 6 digits: 142857num: 1 den: 17 period: 16 digits: 0588235294117647

---

This line may be a bit mysterious:

f"{z // d:0{k}}"

It says: Find the largest integer less than or equal to z divided by d, convert it to a string, and pad it on the left with zeroes (if necessary) to give it a length of k.

---

As Goyo points out in the comments, this algorithm is not perfect. It gets stuck in a loop if the decimal contains any non-repeating part, that is, if the denominator has any factors of 2 or 5. See if you can figure out a way to deal with that.

Solution 2:

This is my Python Implementation of https://www.geeksforgeeks.org/find-recurring-sequence-fraction/

deffraction_to_decimal(numerator, denominator):
    """ This function returns repeating sequence of a fraction.
        If repeating sequence doesn't exits, then returns empty string """# Create a map to store already seen remainders# remainder is used as key and its position in# result is stored as value. Note that we need# position for cases like 1/6.  In this case,# the recurring sequence doesn't start from first# remainder.
    result = ""
    mapping = {}

    # Find first remainder
    remainder = numerator % denominator

    # Keep finding remainder until either remainder# becomes 0 or repeatswhile remainder != 0and remainder notin mapping:

        # Store this remainder
        mapping[remainder] = len(result)

        # Multiply remainder with 10
        remainder = remainder * 10# Append remainder / denominator to result
        result_part = int(remainder / denominator)
        result += str(result_part)
        # print(f"Result: {result}")# Update remainder
        remainder = remainder % denominator
        # print(f"Map: {mapping}")return result

if __name__ == '__main__':
    result = fraction_to_decimal(1, 7)
    if result == "":
        print("No recurring sequence")
    else:
        print(f"\nLenght of recurring sequence: {len(result)}")
        print(f"\nRecurring sequence is {result}\n")