# 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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