The number of times the digit 5 will appear while writing the integers from 1 to 1000 is

To count the number of times the digit 5 appears from 1 to 1000, we can consider its occurrences in each place value:

1. Units Place: The digit 5 appears in the units place for numbers like 5, 15, 25, ..., 995. This occurs once in every block of ten numbers (e.g., 1-10, 11-20, etc.). Since there are 100 such blocks from 1 to 1000 (1000/10 = 100), the digit 5 appears 100 times in the units place.

2. Tens Place: The digit 5 appears in the tens place for numbers like 50-59, 150-159, 250-259, ..., 950-959. In each block of 100 numbers (e.g., 1-100, 101-200, etc.), the digit 5 appears 10 times in the tens place (e.g., 50, 51, ..., 59). There are 10 such blocks from 1 to 1000 (0-99, 100-199, ..., 900-999). So, the digit 5 appears 10 * 10 = 100 times in the tens place.

3. Hundreds Place: The digit 5 appears in the hundreds place for numbers like 500-509, 510-519, ..., 590-599. This covers all numbers from 500 to 599, which is a total of 100 numbers. So, the digit 5 appears 100 times in the hundreds place.

Total occurrences = Occurrences in units place + Occurrences in tens place + Occurrences in hundreds place Total = 100 + 100 + 100 = 300.

Each '5' in a number like 555 is counted distinctly (one for the units, one for the tens, one for the hundreds).

Therefore, the digit 5 will appear 300 times.

The final answer is C) 300.