Question

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

A. 269
B. 300
C. 271
D. 302

Answer 1

To find out how many times the digit 3 will be written from 1 to 1000, we count the occurrences in each place value and add them up, resulting in 302 occurrences, making option D the correct answer.

Step-by-step explanation:

The question asks how many times the digit 3 will appear when we list all the integers from 1 to 1000. This requires us to count the occurrence of the digit 3 in every place value (units, tens, hundreds) separately.

Counting the Digit 3

1. Units place: The digit 3 appears once in every group of ten integers, e.g., 03, 13, 23, ..., 93, totaling to 100 times for 1-1000.
2. Tens place: Similarly, 3 appears ten times in each group of one hundred integers as the tens digit (30, 31, 32, ... 39), totaling to 100 times for 1-1000.
3. Hundreds place: Here, 3 is the hundreds digit for a sequence of 100 numbers (300 to 399), occurring 100 times in total.
4. Extra consideration: We've counted the number 333 once for each place value, so we need to add 2 more to our total to account for the extra 3's in this number.

By adding up the occurrences, we get 100 (units) + 100 (tens) + 100 (hundreds) + 2 (for 333) = 302 times. Therefore, the correct answer is D. 302.