How many digits are in the repeating cycle of 17/27
To find the repeating cycle of a fraction, you need to divide the numerator by the denominator until you get a repeating remainder.
In this case, when you divide 17 by 27, the first remainder is 17. Then, you multiply the remainder by 10 to get 170, and divide this by 27. The remainder is 14. You repeat this process until you find a repeating remainder.
The cycle of remainders for 17/27 is: 17, 14, 17, 14, 17, 14, ...
Thus, the repeating cycle of 17/27 has 2 digits, which are 17 and 14.
To determine how many digits are in the repeating cycle of the fraction 17/27, we need to divide the numerator by the denominator using long division. Let's go step by step:
1. Start by dividing 17 by 27 using long division. The first digit of the quotient is 0 since 17 < 27.
0.
2. Multiply the quotient digit (0) by the denominator (27), and subtract the result (0) from the numerator (17):
17 - 0 = 17
3. Bring down the next digit of the numerator (0).
170
4. Divide 170 by 27. The quotient is 6 since 27 * 6 = 162, and 170 - 162 = 8.
0.6
5. Multiply the quotient digit (6) by the denominator (27) and subtract the result (162) from the numerator (170):
170 - 162 = 8
6. Bring down the next digit of the numerator (0).
80
7. Divide 80 by 27. The quotient is 2 since 27 * 2 = 54, and 80 - 54 = 26.
0.62
8. Multiply the quotient digit (2) by the denominator (27) and subtract the result (54) from the numerator (80):
80 - 54 = 26
9. Bring down the next digit of the numerator (0).
260
10. Divide 260 by 27. The quotient is 9 since 27 * 9 = 243, and 260 - 243 = 17.
0.629
11. Multiply the quotient digit (9) by the denominator (27) and subtract the result (243) from the numerator (260):
260 - 243 = 17
12. Bring down the next digit of the numerator (0).
170
The remainder (17) repeats after this point, and the repeating cycle of the decimal representation of 17/27 starts from here. Thus, the repeating cycle is "629" and contains 3 digits.