The digit 3 can appear in three different positions: units place, tens place, and hundreds place. Each position is counted separately.
In the units place, the digit 3 appears in: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93
This pattern occurs 10 times within each group of 100 numbers.
From 1 to 1000, there are 10 complete groups of 100.
Total 3's in units place =10×10=100
In the tens place, the digit 3 appears in: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39
This pattern occurs once in each group of 100 numbers (130-139, 230-239, 330-339, etc.)
Each occurrence contains 10 numbers.
Total 3's in tens place =10×10=100
In the hundreds place, the digit 3 appears in all numbers from 300 to 399.
This gives 100 consecutive numbers.
Total 3's in hundreds place =100
The number 1000 contains no digit 3.
Total appearances =100+100+100
Total appearances =300
Therefore, the digit 3 appears 300 times when counting from 1 to 1000.