What is the value of $\lceil-4.6\rceil $?
Answer (1)
The ceiling function, denoted by ⌈ x ⌉ , gives the smallest integer greater than or equal to x .
For x = − 4.6 , identify the surrounding integers: − 5 and − 4 .
Determine that − 4 is the smallest integer greater than or equal to − 4.6 .
Therefore, ⌈ − 4.6 ⌉ = − 4 .
Explanation
Understanding the Ceiling Function We are asked to find the value of ⌈ − 4.6 ⌉ , which represents the ceiling of − 4.6 . The ceiling function returns the smallest integer that is greater than or equal to the given number.
Identifying Nearby Integers To find the ceiling of − 4.6 , we need to identify the integers that are close to − 4.6 . These are − 5 and − 4 .
Determining the Ceiling Now, we need to determine which of these integers is the smallest integer that is greater than or equal to − 4.6 . Since -4.6"> − 4 > − 4.6 and − 5 < − 4.6 , the smallest integer greater than or equal to − 4.6 is − 4 .
Final Answer Therefore, ⌈ − 4.6 ⌉ = − 4 .
Examples
The ceiling function is useful in many real-life scenarios. For example, if you need to ship a package that weighs 4.6 pounds, the shipping company might charge you based on the ceiling of the weight. In this case, you would be charged for 5 pounds, even though the package weighs less than that. This ensures that the company is compensated for any additional weight that the package might have.
