Rational Numbers in Different Forms Practice Complete this assessment to review what you've learned. It will not count toward your grade. 1 of 51 of 5 Items Question How many digits are in the repeating cycle of 17/27 ?(1 point)

Answer 1

To find how many digits are in the repeating cycle of the fraction \( \frac{17}{27} \), we can perform long division to express it as a decimal.

When we divide 17 by 27, we note that 27 goes into 17 zero times, so we extend to \( 170 \):

1. 27 into 170 goes 6 times because \( 27 \times 6 = 162 \).

   • Subtract: \( 170 - 162 = 8 \).

2. Bring down a 0 to make it \( 80 \):

   • 27 into 80 goes 2 times because \( 27 \times 2 = 54 \).
   • Subtract: \( 80 - 54 = 26 \).

3. Bring down a 0 to make it \( 260 \):

   • 27 into 260 goes 9 times because \( 27 \times 9 = 243 \).
   • Subtract: \( 260 - 243 = 17 \).

At this point, we've reached \( 17 \) again, which means the numbers will start repeating.

The decimal representation of \( \frac{17}{27} \) is \( 0.629629629...\), where \( 629 \) is the repeating sequence.

Therefore, the repeating cycle of \( \frac{17}{27} \) consists of 3 digits (629).

Final Answer: 3 digits.