Question

How many digits are in the repeating cycle of 1727?(1 point)

Answer 1

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

Answer 2

How many digits are in the repeating cycle of 1727?(1 point)

Answer 3

To determine the repeating cycle of a number, we need to find the remainder when dividing 1 by the number. Let's do the long division process to find the repeating cycle of 1727:

```
0. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 7 2 7 0
-1 7 2 7
0 0 7 2

```
After the first division, we get a remainder of 072. Continuing the process, we have:

```
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 7 2 7 0
-1 7 2 7
0 0 7 2
- 1 7 2
2 5 0
- 2 4 2
6 0

```
Since we obtained the same remainder 072 after the second division, we can conclude that the repeating cycle of 1727 is 072. Therefore, the repeating cycle of 1727 has 3 digits. Answer: \boxed{3}.

Answer 4

To find the repeating cycle of 17/27, we perform long division as follows:

```
0. 6 3 0 6 3 0 6 3 0 6 3 0 6 3 0 6 3 0 6 3
27 | 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 8
-1 7
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
1 0
- 9
```

As we can see, the remainder of each division is 10. Hence, the repeating cycle of 17/27 is 10. Therefore, the repeating cycle of 17/27 has 2 digits. Answer: \boxed{2}.