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 From B. Lee Clay

Squaring Numbers

1. beginning with 1
2. beginning with 5
3. beginning with 9
4. ending in 1
5. ending in 2
6. ending in 3
7. ending in 4
8. ending in 5
9. ending in 6
10. ending in 7
11. ending in 8
12. ending in 9
13. made up of 1's
14. made up of 3's
15. made up of 6's
16. made up of 9's
17. in the 20's
18. in the 30's
19. in the 40's
20. in the 50's
21. in the 60's
22. in the 70's
23. in the 80's
24. in the 100's
25. in the 200's
26. in the 300's
27. in the 400's
28. in the 500's
29. in the 600's
30. in the 700's
31. between 800-810
32. in the 900's
33. between 1000-1100
34. between 2000-2099
35. between 3000-3099
36. between 4000-4099
37. between 5000-5099
38. between 6000-6099
39. between 7000-7099
40. 3's and final 1
41. 3's and final 2
42. 3's and final 4
43. 3's and final 5
44. 3's and final 6
45. 3's and final 7
46. 3's and final 8
47. 3's and final 9
48. 6's and final 1
49. 6's and final 2
50. 6's and final 3
51. 6's and final 4
52. 6's and final 5
53. 6's and final 7
54. 6's and final 8
55. 6's and final 9
56. 9's and final 1
57. 9's and final 2
58. 9's and final 3
59. 9's and final 4
60. 9's and final 5
61. 9's and final 6
62. 9's and final 7
63. 9's and final 8
64. 1 and repeating 3's
65. 1 and repeating 6's
66. 1 and repeating 9's
67. 2 and repeating 3's
68. 2 and repeating 6's
69. 2 and repeating 9's
70. 3 and repeating 6's
71. 3 and repeating 9's
72. 4 and repeating 3's
73. 4 and repeating 6's
74. 4 and repeating 9's
75. 5 and repeating 3's
76. 5 and repeating 6's
77. 5 and repeating 9's
78. 6 and repeating 3's
79. 6 and repeating 9's
80. 7 and repeating 3's
81. 7 and repeating 6's
82. 7 and repeating 9's
83. 8 and repeating 3's
84. 8 and repeating 9's
85. 9 and repeating 3's
86. 9 and repeating 6's
87. 6-digits repeating
88. 2 rep./sq. of 1 digit

Multiplying Numbers

Dividing Numbers

Adding Numbers

Subtracting Numbers

Finding Percents

Calculation
Practice Exercises

Full List

### Squaring special numbers(9's and final 3)

1. Choose a number with repeating 9's and a final 3.
2. The square is made up of:
• one fewer 9 than there are repeating 9's
• 86
• the same number of 0's as there are 9's in the square
• A final 49

#### Example:

1. If the number to be squared is 9993:
2. The square has:

```one fewer 9 than the    repeating 9's:         9 9 86                            8 6 same number of 0's as 9's    in the square                  0 0 a final 49                            4 9```

3. So 9993 × 9993 = 99860049.

See the pattern?

1. If the number to be squared is 999993:
2. The square has:

```one fewer 9 than the    repeating 9's:      9 9 9 9 86                             8 6 same number of 0's as 9's    in the square                   0 0 0 0 a final 49                                 4 9```

3. So 999993 × 999993 = 999986000049.

Using this pattern you will be able to square these large numbers with ease.

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26 April 1999
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