1 / 999…9 = 0.000… 1 000… 1 ……

The former has n 9s, followed by (n- 1) 0s and a cycle of 1.

This fact can be simply verified vertically by division.

From this, we can write any cyclic decimal as a fraction.

For example:

1.04232323……

= 1 + 0.04 + 0.002323……

= 1 + 1 / 25 + (23 / 99) / 100

= 103 19 / 9900

On the contrary, for any fraction, we only need to find the minimum factor of 99 ... 9 to know its cycle segment.

For example: 16 9:

9999999999999999 = 3 × 3 × 1 1 × 17 × 73 × 10 1 × 137 × 5882353

Is the smallest multiple of 17, and the shape is 999...9.

So,

1 / 17

= 0.0588235294 1 17647 0588235294 1 17647 0588235294 1 17647 0588235294 1 17647 0588235294 1 17647 …………

The circular part has 16 position.