Shesanyankena Charamena- "The remainders by the last digit" Consider: 1/7. When divising 1(0) by 7 the remainder is 3. Therefore, dividing 3 by 7 will subsequently lead to remainder 9 (= 3x3). But since 9 is more than 7 the remainder would be 2, so the remainder sequence is: 3, 2Now 2 divided by 7 will have remainder of 6 (3x2), that is 3, 2, 6Continuing 3, 2, 6, 4, 5, 1We stop when the remainder sequence starts to repeat. Now, multiply these remainders by the last digit (7) of the denominator and keep only the first digit (LSD). So we have: 7x3 = 21 => put down 1.1 3, 2, 6, 4, 5, 17x2 = 14 => put down 4.1 4 3, 2, 6, 4, 5, 17x6 = 42 => put down 2.1 4 2 3, 2, 6, 4, 5, 1Continuing.1 4 2 8 5 7 3, 2, 6, 4, 5, 1So the answer is 1/7 = .142857142857..........