Question

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

Hint:

In the range $1$ to $10^n$, each digit (except 0) appears $n \cdot 10^{n-1}$ times.

Answer 1

Correct Answer: 300

Step 1: Consider all numbers from 000 to 999 (1000 numbers).
Step 2: Total digits written $= 1000 \text{ numbers} \times 3 \text{ places} = 3000 \text{ digits}$.
Step 3: Since each digit (0-9) appears with equal frequency:
Step 4: Frequency of digit '3' $= 3000 / 10 = 300$.
Step 5: (The number 1000 does not contain digit 3, so the count remains 300).