Final answer:
The student's question is about the place values of digits in a four-digit number where all digits are the same. The value of the hundreds place is 100, which implies the digit is 1. The number Eileen is thinking of must be 1111, as no other options provided are valid given the place value system.
Step-by-step explanation:
The question involves understanding the place value of a number, which indicates the value of a digit based on its position within a number. In the context of the question, we are dealing with a four-digit number where all digits are the same and the value of the hundred's place digit is 100. This means we are considering the number 1 in the hundred's place, which contributes a value of 100 to the overall number.
Let's examine the options given:
(a) The digit in the tens place is 10. This is incorrect because the value of the digit in the tens place is 10 times its face value, not 10 itself.(b) The digit in the ones place is 100. This is not possible because the highest value a single digit in the ones place can have is 9.(c) The digit in the tens place is 100. This is also incorrect as the value of the tens place cannot be 100; it is the place value that is 10, not the digit's value.(d) The digit in the ones place is 10. Again, this is incorrect because the value of a digit in the ones place cannot exceed 9, and the place value is 1, not 10.
Since all digits are the same, and the digit in the hundreds place represents a value of 100, the four-digit number Eileen is thinking of must be 1111 because 1 in the hundreds place represents 1 x 100, i.e., 100.