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 $10^n$ , 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 $\overline {aa}$ . So, by multiplying an $n$ digit number $a$ with $10^n+1$ , we get the number $\overline {aa}$ . In this example, by multiplying $715$ with $1001$ we get $715715$ .