magical repeating decimal with vedic maths.pptx

magical repeating decima with vedic maths

1. Magical Repeating Decimals with Vedic Math Using Ekadhikena Purvena to Decode 1/19, 1/29, ...

2. Name :- Jadeja Nanditaba Subject Name :- Vedic Mathematics and Its application in Modern Computing 2

3. What Are Repeating Decimals? A repeating decimal has digits that continue forever in a pattern. Example: 1/3 = 0.333... (3 repeats forever). Some fractions have repeating patterns, others don’t This presentation explores a Vedic way to find such patterns easily using Ekadhikena Purvena .

4. Function to Find Repeating Decimals Start with remainder = 1 Multiply by 10, divide by n → Get digit Store remainder each time If same remainder appears again → Cycle starts! Output: decimal + repeating part inside ( )

5. First Example :- Example 1 – 1/19 def find_repeating_decimal (n, max_digits =50): remainder = 1 remainders = {} result = "" position = 0 while position < max_digits : if remainder in remainders: repeat_start = remainders[remainder] return result, result[ repeat_start :] remainders[remainder] = position remainder *= 10 digit = remainder // n result += str(digit) remainder = remainder % n position += 1 return result, "“ decimal_digits , repeating_part = find_repeating_decimal (29, 50) print("Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena '") print(f"1/19 = 0.({ repeating_part })") OUT PUT :- Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena ' 1/19 = 0.(052631578947368421)

6. Second Example :- Example 1 – 1/29 def find_repeating_decimal (n, max_digits =50): Args : n (int): Denominator max_digits (int): Digits to compute Returns: tuple: (full decimal string, repeating part) """ remainder = 1 remainders = {} result = "" position = 0 while position < max_digits : if remainder in remainders: repeat_start = remainders[remainder] return result, result[ repeat_start :] remainders[remainder] = position remainder *= 10 digit = remainder // n result += str(digit) remainder = remainder % n position += 1 return result, "" decimal_digits , repeating_part = find_repeating_decimal (29, 50) print("Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena '") print(f"1/29 = 0.({ repeating_part })") OUT PUT :- Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena ' 1/29 = 0.(0344827586206896551724137931)

7. Third Example :- Example 1 – 1/39 def find_repeating_decimal (n, max_digits =50): Args : n (int): Denominator (e.g., 39) max_digits (int): Number of digits to compute (default is 50) Returns: tuple: (all decimal digits, repeating cycle) """ remainder = 1 remainders = {} result = "" position = 0 while position < max_digits : if remainder in remainders: repeat_start = remainders[remainder] return result, result[ repeat_start :] remainders[remainder] = position remainder *= 10 digit = remainder // n result += str(digit) remainder %= n position += 1 return result, "" decimal_digits , repeating_part = find_repeating_decimal (39, 50) print("Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena '") print(f"1/39 = 0.({ repeating_part })") OUT PUT :- Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena ' 1/39 = 0.(025641)

8. Fourth Example :- Example 1 – 1/49 def find_repeating_decimal (n, max_digits =50): remainder = 1 remainders = {} result = "" position = 0 while position < max_digits : if remainder in remainders: repeat_start = remainders[remainder] return result, result[ repeat_start :] remainders[remainder] = position remainder *= 10 digit = remainder // n result += str(digit) remainder %= n position += 1 return result, "" decimal_digits , repeating_part = find_repeating_decimal (49, 50) print("Repeating Decimal Expansion using Vedic Sutra ' Ekādhikena Pūrvena '") print(f"1/49 = 0.({ repeating_part })") OUT PUT :- a Decimal Expansion using Vedic Sutra ' Ekdhikena Purvena ’ 1/49 = 0.(0204081632653061224489795918367346938775510204081632)

9. Third Example :- Example 1 – 1/59 def find_repeating_decimal (n, max_digits =50): Args : n (int): Denominator (like 59) max_digits (int): Digits to extract Returns: tuple: (full decimal string, repeating part) """ remainder = 1 remainders = {} result = "" position = 0 while position < max_digits : if remainder in remainders: repeat_start = remainders[remainder] return result, result[ repeat_start :] remainders[remainder] = position remainder *= 10 digit = remainder // n result += str(digit) remainder %= n position += 1 return result, "" decimal_digits , repeating_part = find_repeating_decimal (59, 50) print("Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena '") print(f"1/59 = 0.({ repeating_part })") OUT PUT :- Repeating Decimal Expansion using Vedic Sutra ‘ Ekadhikena Purvena ' 1/59 = 0.(0169491525423728813559322033898305084745762711864406779661)

10. Summary Table Fraction Repeating Part (short) Cycle Length 1/19 0.(052631...) 18 digits 1/29 0.(034482...) 28 digits 1/39 0.(025641) 6 digits 1/49 0.(020408...) 42 digits 1/59 0.(016949...) 58 digits

11. Thank you