<p>The total number of times, the digit 3 will be written, when the integers having less than 4 digits are listed is equal to</p>
Step-by-Step Solution
Key Concept: Count digit 3's by position (units, tens, hundreds) across all numbers from 1 to 999, recognizing that each position follows a cyclical pattern with frequency of 100 occurrences per 1000 numbers.
<p><strong>Step 1:</strong> We need to count digit 3 in all integers from 1 to 999 (less than 4 digits).</p><p><strong>Step 2:</strong> Count by position:</p><p><strong>Units place (3, 13, 23, ..., 993):</strong> Digit 3 appears once every 10 numbers. From 1-999: ⌊999/10⌋ = 99 complete cycles + 1 (the 3 itself) = 100 times</p><p><strong>Tens place (30-39, 130-139, ..., 930-939):</strong> Digit 3 appears 10 times per 100 numbers. From 1-999: 9 × 10 + 10 = 100 times</p><p><strong>Hundreds place (300-399):</strong> Digit 3 appears 100 consecutive times</p><p><strong>Step 3:</strong> Total = 100 (units) + 100 (tens) + 100 (hundreds) = 300</p><p>∴ Answer: A</p>
Correct Answer: A