Final answer:
Counting the digit 3's occurrence throughout the range from 1 to 1000, we find it appears 100 times in each the units, tens, and hundreds places, which sums to 300 occurrences. Hence, the digit 3 will be written 300 times when listing integers from 1 to 1000.
Step-by-step explanation:
The question at hand is a common type of problem in mathematics that involves counting the occurrence of a specific digit within a given range of numbers.
Specifically, the problem asks for the number of times the digit 3 will be written when listing all integers from 1 to 1000. To solve this, we consider the number of 3's appearing in each position (units, tens, hundreds) separately and then sum those occurrences.
- There are 10 occurrences of 3 for each hundred numbers (3, 13, 23, ..., 93), so since 1000 has 10 sets of 100, we get 10 * 10 = 100 occurrences in the units place.
- For the tens place, 3 will also appear 10 times for each hundred numbers (30-39, 130-139, ..., 930-939), adding another 100 occurrences.
- For the hundreds place, 3 will appear 100 times in the range 300-399.
- Adding these together gives us 100 + 100 + 100, which totals to 300 occurrences of the digit 3 from 1 to 1000.
Therefore, the correct answer is 300 times that the digit 3 will be written when listing the integers from 1 to 1000.