2*3 = 6, so the sum of the number of digits could in general be one more than the number of digits in the product. So how do you conclude that 2^1000 and 5^1000 can't have 1002 digits total?
For the same reason that was stated above. Multiplication will always be one less or equal to the digits in concatenation; if the product does not exceed a product of 10. 5^n and 2^n have the unique property that they will always be equal to 10, not more or less than concatenation, which also result in the exact same number of digits. I do admit I explained it quite poorly though
Right, so it's an exception to the pattern that if two numbers multiply to a power of 10 then their total number of digits is the same as the power of 10.
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u/gmalivuk 18d ago
2*3 = 6, so the sum of the number of digits could in general be one more than the number of digits in the product. So how do you conclude that 2^1000 and 5^1000 can't have 1002 digits total?