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Absolute Value Calculator



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Understanding Absolute Value

The absolute value of a number represents its distance from zero on the number line, regardless of its direction. This value is always non-negative and is denoted by two vertical bars, as in \( |n| \).

The formula for calculating the absolute value is:

\( |n| \)

where:

  • n is any real number, either positive or negative.

The absolute value is useful in various situations where only the magnitude of a number is needed, such as measuring distances, errors, or deviations.

Examples

The following examples demonstrate how to calculate the absolute value in creative contexts.

1. A submarine dives 300 meters below sea level. What is the absolute value of its depth?

Answer

Given:

  • n = -300 meters (since it's below sea level)

The absolute value of -300 meters is calculated as:

\( | -300 | = 300 \text{ meters} \)

Even though the submarine is below sea level, the absolute value represents the distance from sea level, which is 300 meters.

2. During a game, a player gains 15 points and then loses 20 points. What is the absolute value of the player's net score?

Answer

Given:

  • n = 15 - 20 = -5 points (net score)

The absolute value of -5 points is calculated as:

\( | -5 | = 5 \text{ points} \)

While the player’s net score is negative, the absolute value shows the magnitude of the change, which is 5 points.

3. The temperature drops to -10°C overnight. What is the absolute value of the temperature drop?

Answer

Given:

  • n = -10°C

The absolute value of -10°C is calculated as:

\( | -10 | = 10 \text{°C} \)

The absolute value represents the magnitude of the temperature drop, which is 10°C.

4. An elevator moves 7 floors up and then 3 floors down. What is the absolute value of the elevator's final position relative to its starting point?

Answer

Given:

  • n = 7 - 3 = 4 floors

The absolute value of 4 floors is calculated as:

\( | 4 | = 4 \text{ floors} \)

Since the elevator’s final position is positive, the absolute value remains 4 floors.

Formula

To calculate the absolute value, you can use the following formula.

\( = \) \( | n | \)

Calculation

Once you enter the input values in the calculator, the output parameters are calculated.