What is the value of $\lfloor-1.1\rfloor$?
Answer (1)
The problem requires finding the floor of -1.1, denoted as ⌊ − 1.1 ⌋ .
The floor function returns the greatest integer less than or equal to the given number.
For -1.1, the greatest integer less than or equal to it is -2.
Therefore, ⌊ − 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.
Definition of Floor Function The floor function, denoted by ⌊ x ⌋ , returns the greatest integer that is less than or equal to x . In simpler terms, it rounds the number down to the nearest integer.
Finding the Greatest Integer To find ⌊ − 1.1 ⌋ , we need to identify the greatest integer that is less than or equal to -1.1. On the number line, -1.1 lies between -2 and -1. The integers less than -1.1 are -2, -3, -4, and so on.
Determining the Value The greatest among these integers is -2. Therefore, ⌊ − 1.1 ⌋ = − 2 .
Examples
The floor function is used in computer science to determine the index of an array or a list. For example, if you have an array and you want to access an element based on a floating-point number, you can use the floor function to convert the floating-point number to an integer index. Another example is in everyday life when calculating how many full boxes are needed to pack a certain number of items. If you have 10.7 items, you would need ⌊ 10.7 ⌋ = 10 full boxes, but you would still need an extra box for the 0.7 item.
