Absolute value - Examples, Exercises and Solutions

These signs in the exercises refer to the concept of "absolute value",

In absolute value we don't have "negative" or "positive", instead we measure the distance from point 0,

In other words, we always "cancel out" the negative signs.

In this exercise, we'll change the minus to a plus sign, and simply remain with 19 and a quarter.

And that's the solution!

The "absolute value" can be viewed as the distance of a number from 0.
Therefore, the absolute value will not change the sign from negative to positive, it will always be positive.

To find the absolute value of $0.8$, we will use the definition of absolute value, which states:

• If a number $x$ is positive or zero, then its absolute value is the same number: $|x| = x$.
• If a number $x$ is negative, then its absolute value is the positive version of that number: $|x| = -x$.

Let's apply this to our problem:

Since $0.8$ is a positive number, its absolute value is simply itself:

$|0.8| = 0.8$

Therefore, the absolute value of $0.8$ is $0.8$.

Looking at the given answer choices:

• Choice 1: "There is no absolute value" is incorrect, as every real number has an absolute value.
• Choice 2: $-0.8$ is incorrect, because absolute values are never negative.
• Choice 3: $0$ is incorrect, as the number is not zero.
• Choice 4: $0.8$ is correct, as it matches the calculated absolute value.

Thus, the correct choice is $0.8$.

Therefore, the solution to the problem is $0.8$.

To solve this problem, we will determine the absolute value of the number 3:

• Step 1: Recognize that the number given is 3, which is a positive number.
• Step 2: According to the rules of absolute values, the absolute value of a positive number is the number itself.
• Step 3: Therefore, $|3| = 3$.

In conclusion, the absolute value of 3 is $\mathbf{3}$.

When we have an exercise with these symbols || we understand that it refers to absolute value.

Absolute value does not relate to whether a number is positive or negative, but rather checks how far it is from zero.

In other words, 2 is 2 units away from zero, and -2 is also 2 units away from zero,

Therefore, absolute value essentially "zeroes out" the negativity of the number.

|-2| = 2