What is the absolute value of [tex]$|-287|$[/tex]?
Answer (1)
The problem asks to find the absolute value of ∣ − 287∣ .
Recall that the absolute value of a number is its distance from zero.
Since − 287 < 0 , we have ∣ − 287∣ = − ( − 287 ) .
Simplify to get the final answer: 287 .
Explanation
Understanding the problem We are asked to find the absolute value of ∣ − 287∣ . The absolute value of a number is its distance from zero on the number line. It is always non-negative.
Applying the definition of absolute value The absolute value of a number x , denoted as ∣ x ∣ , is defined as follows:
∣ x ∣ = x if x ≥ 0 ∣ x ∣ = − x if x < 0
In our case, we want to find the absolute value of − 287 . Since − 287 is less than 0, we use the second part of the definition: ∣ − 287∣ = − ( − 287 ) .
Simplifying the expression Now we simplify the expression − ( − 287 ) . The negative of a negative number is the positive of that number. Therefore, − ( − 287 ) = 287 .
Final Answer Thus, the absolute value of ∣ − 287∣ is 287.
Examples
Absolute values are used in many real-life situations. For example, when measuring the error in a manufacturing process, we are often interested in the magnitude of the error, not its direction. If a machine is supposed to cut a metal rod to 10 cm, and it cuts it to 9.8 cm, the error is -0.2 cm. However, the absolute error is |-0.2| = 0.2 cm, which tells us the size of the deviation from the desired length. Similarly, in navigation, the absolute value is used to calculate distances, regardless of direction.
