Squaring special numbers (4 and repeating 9’s)

Follow the following Steps:

  1. Choose a number with a 4 and repeating 9’s.
  2. The square is made up of:

    • first digits: 24 & one fewer 9 than repeating 9’s in the number
    • next digits: same number of 0’s as repeating 9’s in the number
    • last digit: 1

   Example:

  1. If the number to be squared is 4999:
  2. The square has:
    first digits: 24 and one fewer
      9 than 9's (in the number)      2 4 9 9
    next digits: same number of 0's
      as 9's (in the number)                  0 0 0
    last digit: 1                                    1

  3. So 4999 × 4999 = 24,990,001.
   See the pattern?
  1. If the number to be squared is 499999:
  2. The square has:
    first digits: 24 and one
      fewer 9 than 9's          2 4
    9 9 9 9
    next digits: same number
      of 0's as 9's                        0
    0 0 0 0
    last digit: 1                                    1

  3. So 499999 × 499999 = 249,999,000,001.