This question asks us to determine the last incomplete natural number that a device was writing after being operated for half an hour. We are given that the device can write 100 digits in 1 minute.

To find the last incomplete number, we need to calculate how many numbers can be written in half an hour.

There are 60 minutes in an hour, so half an hour would be 30 minutes.

Since the device can write 100 digits in 1 minute, we can write 100 x 30 = 3000 digits in 30 minutes.

However, the last number written is incomplete. This means that we need to find the largest number that is less than or equal to 3000 and has an incomplete representation.

Option 1, 3000, is a complete number and not the correct answer.

Option 2, 3001, is not a valid number since it exceeds the 3000 limit.

Option 3, 1026, is also not a valid answer since it is less than 3000.

Therefore, the correct answer is option 4, 1027, which is the largest incomplete number less than or equal to 3000.