To find how many digits are in the repeating cycle of the decimal representation of \( \frac{17}{27} \), we can first perform the division.
When we divide \( 17 \) by \( 27 \), we find:
\[ 17 \div 27 = 0.629629629\ldots \]
We can see that the decimal representation has a repeating cycle.
To determine the length of the repeating part, we can express \( \frac{17}{27} \) as a decimal. The decimal expansion is \( 0.\overline{629} \), indicating that "629" repeats indefinitely.
Thus, the length of the repeating cycle of \( \frac{17}{27} \) is 3 digits.
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