How does the near-100 method handle numbers above 100, and what if the right part overflows?

Use surpluses instead of shortfalls (and add); if the right part exceeds two digits, carry the extra into the left part.

• Above 100: 103 × 104 → surpluses +3, +4 → left 103 + 4 = 107, right 3 × 4 = 12 → 10712. (Check: 10712 ✓.)
• Right-part carry: 88 × 88 → shortfalls −12, −12 → left 88 − 12 = 76, right 12 × 12 = 144 → but the right slot holds only 2 digits, so carry the 1: 76 + 1 = 77, right 44 → 7744. (Check: 88² = 7744 ✓.)

The right part always has as many digits as the base has zeros (2 for base 100); anything extra carries left.