999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999•9999999999999999999999999999999999999999999999999999999999999999999999999999999999999…

It looks like you’re multiplying two numbers that are each a string of 9s, separated by a multiplication dot.

• If both numbers have the same length n (i.e., both are 99...9 with n digits), then: (10^n − 1)(10^n − 1) = 10^(2n) − 2·10^n + 1 In decimal this is: (n−1) copies of 9, then an 8, then (n−1) copies of 0, then 1. Examples:

  • n = 1: 9 × 9 = 81
  • n = 2: 99 × 99 = 9801
  • n = 3: 999 × 999 = 998001

• If the two numbers have different lengths, say n digits and m digits, then: (10^n − 1)(10^m − 1) = 10^(n+m) − 10^n − 10^m + 1 The decimal pattern is less uniform, but this formula gives the exact value.

If you tell me the exact number of digits in each factor (i.e., how many 9s are in each), I can give you the exact product (or print the full digit sequence for you).