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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 (6 and
                 repeating 9's)

  1. Choose a number with a 6 and repeating 9's.
  2. The square is made up of:
    • first digits: 48 & two fewer 9's than repeating 9's in the number
    • next digits: 86 & one fewer 0 than repeating 9's in the number
    • last digit: 1

   Example:

  1. If the number to be squared is 6999:
  2. The square has:

    first digits: 48 and two fewer
        9's than rep. 9's            4 8 9
    next digits: 86 and one fewer
        0 than rep. 9's                   8 6 0 0
    last digit: 1                                 1

  3. So 6999 × 6999 = 48,986,001.

   See the pattern?

  1. If the number to be squared is 699999:
  2. The square has:

    first digits: 48 and two fewer
       9's than rep. 9's      4 8 9 9 9
    next digits: 86 and one fewer
       0 than rep. 9's                 8 6 0 0 0 0
    last digit: 1                                  1

  3. So 699999 × 699999 = 489,998,600,001.
     


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15 March 1999
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