How many digits are in the repeating cycle of 17/27??
To determine the repeating cycle of a fraction, we divide the numerator by the denominator and observe the remainder.
When we divide 17 by 27, we get a quotient of 0 and a remainder of 17.
We then multiply the remainder by 10 and divide by the denominator again. This gives us 17 x 10 = 170 / 27 = 6 remainder 8.
We continue this process until the remainder becomes zero or until we observe a repeating cycle.
Next, we multiply the latest remainder (8) by 10 and divide by 27. This gives us 8 x 10 = 80 / 27 = 2 remainder 26.
Multiplying the remainder (26) by 10 and dividing by 27, we get 26 x 10 = 260 / 27 = 9 remainder 17.
Continuing this process, we find that multiplying the remainder (17) by 10 and dividing by 27 gives us 17 x 10 = 170 / 27 = 6 remainder 8. This is a repeated remainder.
Therefore, the repeating cycle of the fraction 17/27 is 8, 26, 17, 8, 26, 17, ...
We can see that the repeating cycle consists of 8, 26, and 17.
So, there are three digits in the repeating cycle of 17/27.