How many digits are in the repeating cycle of 17 over 27
To find the repeating cycle of a fraction, you need to perform long division.
When you divide 17 by 27, the quotient is 0.629 and the remainder is 17.
To continue the long division, we bring down a zero after the decimal point and divide 170 by 27. The quotient is 6.296, and the remainder is 22.
We continue this process by bringing down another zero and dividing 220 by 27. The quotient is 8.148, and the remainder is 4.
To continue the long division, we bring down another zero and divide 40 by 27. The quotient is 1.481 and the remainder is 13.
We bring down another zero and divide 130 by 27. The quotient is 4.814, and the remainder is 22.
We bring down another zero and divide 220 by 27. The quotient is 8.148, and the remainder is 4.
It can be observed that the remainder 4 repeats after the 2nd decimal place.
Therefore, the repeating cycle of 17/27 is two digits long.
To find the number of digits in the repeating cycle of a fraction, divide the numerator by the denominator. In this case, the fraction is 17/27.
Divide 17 by 27:
0.6296296296296296...
From the calculations, we can see that the decimal representation of 17/27 will have a repeating cycle of 6 digits: 629629. Therefore, the repeating cycle of the fraction 17/27 has 6 digits.