Counting Recurring Decimal

Level pending

The recurring decimal \(0.\overline{000001002003004005006007008009...993994995996997999000001002}...\) can be written as a fraction \(\frac {a}{b}\) as a fraction in it's lowest terms. \(a\) and \(b\) are also co-prime positive integers. What is the last 3 digits of the sum of \(a\) and \(b\)?

Note : If you think the answer ends in 012, type in 012 Hint : There is a pattern in the decimal arrangement. Look at every group of 3 numbers. The pattern is there apart from at the end

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