100000 x 100 = 10000000
100000 times 100 is 10000000, ten million. Both numbers are powers of ten, so the zeros simply add up: five zeros plus two zeros gives seven, and nothing else needs working out.
100,000 × 100 = 10,000,000
Adding 100,000 to itself 100 times gives the same answer.
Count the zeros, not the digits
100000 is 10 to the fifth power and 100 is 10 to the second. Multiplying powers of the same base adds the exponents, so the answer is 10 to the seventh: a 1 followed by seven zeros, 10000000. Counting digits instead of zeros is where a place goes missing, because 100000 has six digits but only five zeros.
Other routes to ten million
The same answer arrives from a different pair. 10000 x 1000 is also 10000000, since four zeros plus three is seven again. Any split of seven zeros across the two numbers ends up here, which makes this a useful answer to sanity-check others against.
Saying it out loud
10000000 is ten million in the short scale used across English-speaking countries. In the Indian numbering system the same quantity is one crore, grouped as 1,00,00,000 rather than 10,000,000. Same number, different digit grouping.
One step either way
Drop a zero and 10000 x 100 gives 1000000, one million. Add one and 100000 x 1000 gives 100000000, a hundred million.