Absolute Value of a Real Number

|x|, which is expressed as ‘Mod x’ or ‘Modulus of x,’ represents the absolute value of such a variable x. The Latin term ‘modulus’ literally means ‘measure.’ “Numerical value” or “magnitude” are other terms for “absolute value.” The absolute value only reflects the numeric value and does not include the sign of the numeric value. Any vector quantity’s modulus is always positive and equal to its absolute value. Furthermore, absolute values are used to express quantities such as distance, price, volume, & time.

The absolute value of |+5| = |-5| = 5 is an example. Absolute value does not have a sign ascribed to it. In this article, we’ll look at the concept of a number’s absolute value, its symbol, as well as how to calculate it. For a better understanding, we shall solve several examples based on the notion.

What is the definition of absolute value?

A number’s absolute value is its distance from origin (0). As we know that distance is always a positive number. The absolute value of number is always a non-negative integer because it is a distance. 

To describe a rise or decrease in quantity, values above or below the mean value, profit, or loss in a transaction, a positive or negative value is occasionally attributed to a numeric value. In absolute value, the sign of numeric is ignored, and just the numeric value is considered. 

Definition of Absolute Value

The magnitude of a number, regardless of its sign, is defined as its absolute value. We consider only the number and ignore the sign to determine the absolute value of a real number. It can only be a positive number. A positive number’s absolute value is the number itself; a negative number’s absolute value is the number without a negative sign, and 0’s absolute value is 0.

Sign of Absolute Value

We write the vertical bar on either side of a number (or a variable) to denote its absolute value, i.e., |x|, where x is an integer. The absolute value of 4 is denoted as |4|, for example. In addition, the absolute value of -4 is denoted by the symbol |-4|. As previously expressed, the absolute value always yields a non-negative value. As a result, |4|=|-4| =4. As a result, negative integers are converted to positive values. The absolute value sign is depicted in the diagram below.

Number’s Absolute Value:

The absolute value of an integer is always non-negative, as previously mentioned. The absolute value of an integer x is denoted by the symbol |x|, and its formula is |x| = x if x > 0 and |x| = -x if x 0, and |x| = 0 if x = 0. 

|2| = 2 

|-9| = 9 are some examples of absolute value of a number.

Absolute value of 0:

We’ve talked about the absolute value for positive & negative numbers so far. Now we’ll talk about zero’s absolute value. Because 0 has neither a positive nor a negative value, its absolute value is 0. Because the distance between 0 and 0 is zero, we can argue that absolute value of 0 is zero.

Important Points to Remember About Absolute Value

• |x| or abs are used to represent the absolute value of x. (x).
• Any number’s absolute value always yields a non-negative outcome.
• |x| is pronounced ‘mod x’ or’ modulus of x.’

Conclusion:

The generalisation of arithmetic is how algebra is commonly described. We can communicate & solve a wide range of real-world problems by using variables, which are letters that represent numbers. As a result, we begin by looking at real numbers and how they work.

A set is a group of things that are often arranged within braces, with each object being referred to as an element. We concentrate on certain sets of numbers when studying mathematics.

It’s denoted by the symbol |a|, which stands for the magnitude of every integer ‘a’. The absolute value of the any integer, positive or negative, is the actual numbers, regardless of the sign. The modulus of an is represented by two vertical lines |a|, which is also known as the modulus of a.

The modulus symbol, ‘| |’, is used to denote absolute value, with the numbers there between. The absolute value of 9 is expressed as |9|, for example.

The distance between a number as well as the origin just on number line is its absolute value. It also displays the number’s polarity, whether positive or negative. It can never be negative since it represents distance, and distance cannot be negative.