How many digits are in the repeating cycle of 17/27? (1 point)

Answer 1

To determine how many digits are in the repeating cycle of the fraction \( \frac{17}{27} \), we can first compute the decimal representation of the fraction.

1. Divide 17 by 27.

2. The integer part is 0, so we write \( \frac{17}{27} = 0.\overline{x} \), where \( x \) is the repeating part.

3. Perform the long division:

   • 17.000 divided by 27 gives 0.629629629...
   • This division reveals a repeating pattern of '629'.

Since the decimal \( 0.629629629... \) repeats with the digits '629', we see that the repeating cycle is 3 digits long.

Thus, the number of digits in the repeating cycle of \( \frac{17}{27} \) is \( \boxed{3} \).