True or False: The absolute value of ${ }_{10}=10$.
Answer (1)
Understand the definition of absolute value as the distance from zero.
Calculate the absolute value of 10, which is ∣10∣ = 10 .
Compare the calculated value with the statement.
Conclude that the statement is True .
Explanation
Understanding Absolute Value We are asked to determine if the statement 'The absolute value of 10 = 10 ' is true or false. Let's break down what absolute value means.
Definition of Absolute Value The absolute value of a number is its distance from zero on the number line. It is always a non-negative value. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5.
Calculating the Absolute Value of 10 In this case, we need to find the absolute value of 10, which is written as ∣10∣ . Since 10 is a positive number, its distance from zero is simply 10. Therefore, ∣10∣ = 10 .
Determining the Truth Value of the Statement Now we compare the calculated absolute value with the given value in the statement. The statement says that the absolute value of 10 is equal to 10, which is what we found: ∣10∣ = 10 . Therefore, the statement is true.
Final Answer The absolute value of 10 is indeed 10. Therefore, the statement 'The absolute value of 10 = 10 ' is true.
Examples
Absolute values are used in many real-world scenarios. For example, when calculating the error in a measurement, we often use the absolute value to ensure that the error is always a positive value, regardless of whether the measurement is above or below the true value. Another example is in navigation, where the absolute value is used to calculate distances, ensuring that the distance is always positive, regardless of the direction.
