The pattern in the decimal form of ninths

Investigation 1: Is there a pattern in the decimal form of ninths?

Hypothesis:

As 7/9, 0.77777…, and 8/9, 0.88888…, are very similar in their decimal forms, I believe that there will be a pattern in the decimal form of ninths.

Results:

Number of Ninths	Decimal	Does It Follow The Pattern?
1	0.11	Yes
2	0.22	Yes
3	0.33	Yes
4	0.44	Yes
5	0.56	Yes
6	0.67	Yes
7	0.78	Yes
8	0.89	Yes
9	1.00	Yes
10	1.11	Yes
11	1.22	Yes
12	1.33	Yes
13	1.44	Yes
14	1.56	Yes
15	1.67	Yes
16	1.78	Yes
17	1.89	Yes
18	2.00	Yes
19	2.11	Yes
20	2.22	Yes
21	2.33	Yes
22	2.44	Yes
23	2.56	Yes
24	2.67	Yes
25	2.78	Yes
26	2.89	Yes
27	3.00	Yes

Conclusion:

The whole numbers (0, 1 and 2) show the amount of complete nines. For example 9 ninths is equal to 1 complete 9 and 18 ninths is equal to 2. This is why they are shown as 1.00 and 2.00.

The numbers following the decimal place show the fraction of the whole nine remaining. These decimals, except 0, are recurring, making the number infinitely long. However, these numbers have been rounded up and down to 2 decimal places. Numbers like 1.89 and 0.56 have been rounded up and the second decimal is always 1 more than the first. Meanwhile, numbers rounded down repeat the first decimal and include 1.22 and 0.44.

This reveals a pattern in the decimal form of ninths. For 1 to 8 ninths, the recurring number after the decimal place is the same as the amount of ninths. From 10 to 17 ninths, the decimal is 1 more than the amount of ninths shown in the ones column. From 19 to 26 ninths the decimal is two more. 

Investigation 2: Does the pattern in the decimal form of ninths reset?

Hypothesis:

The pattern described above will keep going with the difference between the first decimal and ones column of ninths increasing by 1 after every whole 9 until it reaches 90 ninths. In theory, the pattern should restart here due to 90 being a multiple of 9 that ends in 0.

Results:

Number Of Ninths	Decimal	Does It Follow The Pattern
27	3.00	Yes
28	3.11	Yes
29	3.22	Yes
30	3.33	Yes
31	3.44	Yes
32	3.56	Yes
33	3.67	Yes
34	3.78	Yes
35	3.89	Yes
36	4.00	Yes
37	4.11	Yes
38	4.22	Yes
39	4.33	Yes
40	4.44	Yes
41	4.56	Yes
42	4.67	Yes
43	4.78	Yes
44	4.89	Yes
45	5.00	Yes
46	5.11	Yes
47	5.22	Yes
48	5.33	Yes
49	5.44	Yes
50	5.56	Yes
51	5.67	Yes
52	5.78	Yes
53	5.89	Yes
54	6.00	Yes
55	6.11	Yes
56	6.22	Yes
57	6.33	Yes
58	6.44	Yes
59	6.56	Yes
60	6.67	Yes
61	6.78	Yes
62	6.89	Yes
63	7.00	Yes
64	7.11	Yes
65	7.22	Yes
66	7.33	Yes
67	7.44	Yes
68	7.56	Yes
69	7.67	Yes
70	7.78	Yes
71	7.89	Yes
72	8.00	Yes
73	8.11	Yes
74	8.22	Yes
75	8.33	Yes
76	8.44	Yes
77	8.56	Yes
78	8.67	Yes
79	8.78	Yes
80	8.89	Yes
81	9.00	Yes
82	9.11	Yes
83	9.22	Yes
84	9.33	Yes
85	9.44	Yes
86	9.56	Yes
87	9.67	Yes
88	9.78	Yes
89	9.89	Yes
90	10.00	No
91	10.11	Yes
92	10.22	Yes
93	10.33	Yes
94	10.44	Yes
95	10.56	Yes
96	10.67	Yes
97	10.78	Yes
98	10.89	Yes
99	11.00	Yes

Conclusion:

The table above shows that the pattern does keep going until 90 ninths, with the difference between the ones column of ninths and decimal being 9 between 82 and 89 ninths. Then, the difference resets and becomes 0 once more upon reaching 90 ninths.