A boy claims that he can multiply any three digit no. by 1001 instantly. If his friend said "715", he'd say the answer immediately. Compute the answer and justify.
Credit-" Algebra " by I. M. Gelfand and A. Shen
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If we multiply an n digit number a by 1 0 n , we get n zeros to the right of that number. When we add that number with the product, we get a number of the form a a . So, by multiplying an n digit number a with 1 0 n + 1 , we get the number a a . In this example, by multiplying 7 1 5 with 1 0 0 1 we get 7 1 5 7 1 5 .