22 x 100 = 2200
22 times 100 is 2200. Add two zeros to 22 and you have it. If splitting is easier, 20 times 100 is 2000 and 2 times 100 is 200, and those add to 2200.
22 × 100 = 2,200
Adding 22 to itself 100 times gives the same answer.
The working
Two multiplications by ten take 22 to 220 and then to 2200. The split method gets there too: 2000 from the tens, 200 from the units, added together.
The doubling route
22 is 2 x 11, so this answer is simply double 11 x 100 = 1100. If you already know the eleven times table, doubling is the shortest path to any 22 x n answer, and it avoids the split entirely.
The factor of 11 survives into the product, so 2200 divides by 11 exactly and gives 200. The digit test agrees: alternately adding and subtracting the digits of 2200 gives 2 – 2 + 0 – 0 = 0, and any number whose alternating digit sum is 0 is divisible by 11. Fully broken down, 2200 is 8 x 25 x 11.
2200 read as a time
On a 24-hour clock, 2200 is 10:00 at night. That is the everyday context in which the number appears on its own, rather than as the answer to anything.
The usual slip
22 x 10 is 220, not 2200. One zero decides it. The repeated 2s make the two answers look alike at a glance, which is exactly why the error slips through.