All the odd numbers from 51 to 5001 are written. What is the total number of digits used?
how many 2-digit? 49 (51-99)
how many 3-digit? ...
To find the total number of digits used, we need to count the number of digits in each odd number from 51 to 5001.
To find the total number of digits used in writing all the odd numbers from 51 to 5001, we can follow these steps:
Step 1: Determine the total number of odd numbers in the given range.
To find the number of odd numbers, we need to calculate the difference between the last and first odd numbers in the given range and add 1 to include both endpoints.
First odd number: 51
Last odd number: 5001
Number of odd numbers = (Last odd number - First odd number)/2 + 1
Number of odd numbers = (5001 - 51)/2 + 1
Number of odd numbers = 4965/2 + 1
Number of odd numbers = 2482.5 + 1
Number of odd numbers = 2483
Step 2: Determine the number of digits in each odd number.
Since all the odd numbers between 51 and 5001 are written, we need to calculate the number of digits in each odd number.
Let's analyze the number of digits for different ranges of odd numbers:
- For 1-digit numbers: There are 5 odd numbers ranging from 51 to 59, resulting in 5 digits.
- For 3-digit numbers: There are 50 odd numbers ranging from 101 to 199, resulting in 150 digits.
- For 4-digit numbers: There are 500 odd numbers ranging from 1001 to 1999, resulting in 2000 digits.
- For 5-digit numbers: There are 1933 odd numbers ranging from 2001 to 5001, resulting in 9665 digits.
Step 3: Calculate the total number of digits used.
To find the total number of digits, we need to sum the number of digits for each range of odd numbers.
Total digits = (Number of digits for 1-digit numbers) + (Number of digits for 3-digit numbers) + (Number of digits for 4-digit numbers) + (Number of digits for 5-digit numbers)
Total digits = 5 + 150 + 2000 + 9665
Total digits = 11820
Therefore, the total number of digits used in writing all the odd numbers from 51 to 5001 is 11,820.