How many digits are in the repeating cycle of 1727 ?(1 point)
To find the repeating cycle of a fraction, we can use long division.
Let's divide 1 by 1727:
```
0.0005794571...
_________________
1727 | 1.00000000
- 8635
1365
1075
290
```
We can see that the decimal representation of 1/1727 starts repeating after the remainder becomes 290. Therefore, the repeating cycle of 1727 is 290.
The repeating cycle of 1727 has 3 digits: 2, 9, and 0.
To find the number of digits in the repeating cycle of 1727, we need to convert it into a fraction form.
Since 1727 is a non-repeating decimal, divide it by 9999, which is the largest 4-digit repeating number.
1727 / 9999 ≈ 0.172717...
Thus, the repeating cycle of 1727 has 6 digits.
To find the number of digits in the repeating cycle of 1727, we can use a method called long division.
Step 1: Divide the number 1 by 1727.
0.0005796...
Step 2: Multiply the resulting decimal by 10.
0.005796...
Step 3: Divide the new decimal by 1727.
0.0033585...
Step 4: Multiply the new decimal by 10.
0.033585...
Step 5: Divide the new decimal by 1727.
0.0194959...
Step 6: Multiply the new decimal by 10.
0.194959...
Step 7: Divide the new decimal by 1727.
0.112917...
This process will continue indefinitely. We can observe that the repeating cycle begins at step 4, where we get the decimal number 0.033585... Therefore, the repeating cycle has 6 digits: 033585.
So, the answer is 6 digits.