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Infinitely many. The number pi , for example, is between 1 and 1000 and, since pi is a transcendental number, it contains infinitely many digits. Plus, there are all the Irrational Numbers - each with infinitely many digits, and all the rationals with recurring decimals - again with infinitely many digits.

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Q: How many digits are there in all numbers inclusive from 1 to 1000?
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