How many digits are in the repeating cycle of 17/27? (1 point)
To find the repeating cycle of a fraction, we can use long division.
When we divide 17 by 27 using long division, we get:
___________
27| 17.0000000000000000000000
- 1.620000000000000000000 (27 goes into 17 zero times)
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50.000000000000000000000
-47.000000000000000000000 (27 goes into 50 once)
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30.000000000000000000000
- 27.000000000000000000000 (27 goes into 30 once)
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30.000000000000000000000
- 27.000000000000000000000 (27 goes into 30 once)
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30000000000000000000
We notice that the remainder 3 repeats itself after dividing 17 by 27.
Therefore, the repeating cycle of the fraction 17/27 is 3.
Since the repeating cycle has one digit, the answer is 1.
To determine the number of digits in the repeating cycle of a fraction, we need to find its decimal representation and identify the repeating pattern.
When we divide 17 by 27, the decimal representation is 0.6296296296296296...
As we can see, the digit pattern "629" repeats indefinitely. So the repeating cycle of 17/27 has three digits: 629.