number of digits used and number of zeros used

if one writes the numbers {1,2,3,4,5,...10} one uses 11 digits and 1 zero if one writes the number {1,2,3,4,....100} one uses 192 digits and 11 zeros it is true for the set of numbers as the number of zeros used in {1,2,3,......10^k} is equal to the number of digit used in { 1,2,3,4,....10^(k-1)} , for all k=1,2,3,4,....

#NumberTheory

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$