Question

How many digital are in the repeating cycle of 17/27

Answer 1

To determine the length of the repeating cycle of a fraction in decimal form, we can perform long division.

When we divide 17 by 27, the remainder after the first division is 17. We then multiply the remainder by 10 and continue the process.

```
0.6296296296296296
---------
27| 17.000000000000000
- 16
----------
10.000000000000000
- 9
---------------
100.000000000000000
- 81
---------------
190.000000000000000
- 189
---------------
1000.000000000000000
- 972
---------------
280.000000000000000
- 270
---------------
1000.000000000000000
- 972
---------------
280.000000000000000
- 270
---------------
100
```

We can observe a repeating cycle starting after the first few digits (17). The cycle in this case is 627 with a length of 3 digits. Therefore, the repeating cycle of 17/27 in decimal form has a length of 3 digits.