The number of times the digit 3 will be writt | vedclass

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(B) To find the number of times the digit $3$ appears in integers from $1$ to $1000$,we consider all numbers as $3$-digit numbers (treating $1$ to $99

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$300$

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(B) To find the number of times the digit $3$ appears in integers from $1$ to $1000$,we consider all numbers as $3$-digit numbers (treating $1$ to $999$ as $001$ to $999$ and adding $1000$ separately).For any position (units,tens,or hundreds),if we fix the digit $3$,the other two positions can each be filled by any of the $10$ digits $(0-9)$.Number of times $3$ appears in the units place: $10 	imes 10 = 100$.Number of times $3$ appears in the tens place: $10 	imes 10 = 100$.Number of times $3$ appears in the hundreds place: $10 	imes 10 = 100$.Total occurrences = $100 + 100 + 100 = 300$.The number $1000$ does not contain the digit $3$,so the total count remains $300$.

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

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