What is the value of $\lfloor-1.1\rfloor$?
Answer (1)
Understand the floor function as the greatest integer less than or equal to the given number.
Visualize the number -1.1 on a number line and identify the integers around it.
Determine that the greatest integer less than or equal to -1.1 is -2.
Conclude that ⌊ − 1.1 ⌋ = − 2 .
Explanation
Understanding the Floor Function We are asked to find the value of ⌊ − 1.1 ⌋ , which represents the greatest integer less than or equal to -1.1.
Visualizing on the Number Line To find the greatest integer less than or equal to -1.1, visualize a number line. The integers around -1.1 are -2, -1, 0, and so on.
Determining the Greatest Integer The greatest integer that is less than or equal to -1.1 is -2. Therefore, ⌊ − 1.1 ⌋ = − 2 .
Final Answer Thus, the value of ⌊ − 1.1 ⌋ is − 2 .
Examples
The floor function is used in computer science to determine the index of an array. For example, if you have an array and you want to access an element using a non-integer index, you can use the floor function to round down to the nearest integer index. This ensures that you access a valid element in the array. For instance, if you have an array of size 10 and you want to access the element at index 3.7, ⌊ 3.7 ⌋ = 3 , so you would access the element at index 3.
