Summing digits to a million

MediumCombinatorics Brainteasers~6m

What is the sum of all the digits of all the integers from $1$ to $1{,}000{,}000$ inclusive? (For example, the number $46$ contributes $4 + 6 = 10$ .)

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Pad numbers to $6$ digits ( $000000$ – $999999$ ). In each position every digit $0$ – $9$ appears $100000$ times.
Per position: $100000\cdot45$ ; times $6$ positions; then add the digits of $1{,}000{,}000$ .

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27000001

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Asked at: Jane Street, Citadel

Summing digits to a million

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