What is 999999999999999999999 times 99999999999999999999999999?

Answer 1

The original answer is incorrect. A quick inspection of the sum of the digits reveals that this answer is not a multiple of 9 (since multiplicand and multiplier have all nines as digits, both of them are multiples of nine, so the product has to be a multiple of nine as well).

Here's a way to solve it without trying to multiply out long hand:

999999999999999999999 = (10^21 - 1) and 99999999999999999999999999 = (10^26 - 1).

Now multiply the two binomials using FOIL: 10^47 - 10^21 - 10^26 + 1

Here is the corrected answer:

99,999,999,999,999,999,999,899,999,000,000,000,000,000,000,001

Figure it like this: 10^47 = 99,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999 + 1

10^21 = 999,999,999,999,999,999,999 + 1 and

10^26 = 100,000,000,000,000,000,000,000,000

So subtract 10^21 from 10^47 (using the revised expressions) & you have:

99,999,999,999,999,999,999,999,999,000,000,000,000,000,000,000

Subtract 10^26 and you have:

99,999,999,999,999,999,999,899,999,000,000,000,000,000,000,000

Finally, add 1.

Original answer:

779850964987498765098576850893789679478560370