How many times would I be writing the digit 2 if I wrote down ALL THE NUMBERS from 11 to 199 once?

Answer

To find out how many times the digit '2' appears in all the numbers from 11 to 199, we can break down the ranges of numbers into segments: 11-99 and 100-199. 1. **Counting from 11 to 99:** - **Tens place (20 to 29):** The digit '2' appears in the tens place for each number from 20 to 29, which are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. This gives us 10 occurrences of '2'. - **Units place (2, 12, 22, 32, 42, 52, 62, 72, 82, 92):** The digit '2' appears in the units place for the numbers 12, 22, 32, 42, 52, 62, 72, 82, and 92. This gives us 9 occurrences of '2'. Therefore, from 11 to 99, the digit '2' appears: - In the tens place: 10 times - In the units place: 9 times - **Total from 11 to 99 = 10 + 9 = 19** 2. **Counting from 100 to 199:** - **Hundreds place:** The digit '2' doesn't appear in the hundreds place in this range (100-199). Therefore, it appears 0 times in the hundreds place. - **Tens place (120 to 129):** For the tens place, the digit '2' appears in 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, which counts as 10 occurrences. - **Units place (102, 112, 122, 132, 142, 152, 162, 172, 182, 192):** The digit '2' appears in the units place for the numbers 102, 112, 122, 132, 142, 152, 162, 172, 182, and 192. This gives us 10 occurrences of '2'. Therefore, from 100 to 199, the digit '2' appears: - In the hundreds place: 0 times - In the tens place: 10 times - In the units place: 10 times - **Total from 100 to 199 = 0 + 10 + 10 = 20** Finally, we add the totals from both ranges: - From 11 to 99: 19 times - From 100 to 199: 20 times - **Grand Total = 19 + 20 = 39** Therefore, if you wrote down all numbers from 11 to 199, you would be writing the digit '2' a total of 39 times. The answer is D. 39.