999 + (9/9) = 1000
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999 + 999/999
About 111 times
The sum 9 + 99 + 999 + 9999 + 99 999 + .... where the last number to be added consists of nine digits of 9 becomes: (10 – 1) + (100 – 1) + (1000 – 1) + (10 000 – 1) + ... where the last multiple of 10 has nine zeros. There are nine pairs of brackets altogether. Add the multiples of 10 first and then subtract 9: The digit 1 appears 9 times in the final answer.
5 times
111.1111 x 9