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**Constant|Definition & Meaning**

**Definition**

A **constant** is a **fixed**, unchanging value. For example, in 7x – 3 + 5 = 4, the **constants** are **3**, **5**, and **4**. If the value of a **constant** is **unknown**, we **represent** it as **a**, **b**, **c**, etc., to indicate a fixed value. Even then, they do not behave like variables. However, a **constant** may **change** if the **system’s** conditions **change** (e.g., the boiling point of water changes as the altitude changes).

**Constant in Algebraic Expressions **

Figure 1 – Constant in Algebraic Expressions

In **algebraic** **expressions**, **constants** are **values** or symbols that **don’t** **change** during the computation. They are used to **represent** constant **fixed** **values**, such as “**pi”** or “**e”**, or specific numerical values that are given in a problem.

They can also be used to **represent** **mathematical** **constants**. A constant in an algebraic expression is typically **denoted** by a **letter**, like **“c”** or** “k.” **For instance, the constant number **2** is used to **represent** the **y-intercept** of the line denoted by the equation in the expression **y = 3x + 2.**

**Types of Constants**

Figure 2 – Types of Constant

Numerous types of constants are employed in various contexts in mathematics, including:

**Mathematical Constants**: Constants in mathematics are fixed numerical values that appear in a variety of mathematical formulas, such as**pi or e**.**Physical constants**: These are fixed numbers that stand in for physical constants like the**gravitational constan**t,**Planck’s constant**, and the**speed of light**.**Numerical Constant**: The term “numerical constants” refers to specific numerical values, such as**coefficients**or**arbitrary****parameters**, that are used in a particular problem or calculation.**Constant Function**: Functions that produce a constant value regardless of the input value are known as constant functions. For instance, the constant**function f(x) = 2**always**yields****2**and is referred to as a**constant****function**.**Character Constants**: In computer programming, these symbols or characters are used to represent particular values, such as**single****letters**,**strings**, or**particular****symbols**.

**Constant vs. Variable**

Figure 3 – Difference Between Constant and Variable

**Constant**

A **constant** is a value that **does** **not** **alter** **over** **time** or in response to different input values. Constants in mathematics are frequently denoted by symbols like **pi** , **e**, or by a particular numerical value like **2** or **5**. Constants are used to represent fixed values that do not change, like the **gravitational constant** and the **speed** of **light**.

**Variable**

On the other hand, a **variable** is a value that can **change** or have different values assigned to it. Variables in mathematics are frequently **denoted** by letters like **x, y, or z**. For example, a **person’s** **height** or the number of **apples** in a basket are examples of values that can vary and are represented by variables.

In a nutshell, the primary distinction between constants and variables is that the **former** has **fixed** **values** that do not change, whereas the **latter** has **variable** **values**. **Variables** are used to **represent** **values** that can **change**, whereas **constants** are used to **represent** **fixed** **values**.

**Properties of Constants**

Following are a few properties of constants:

**Fixed Value**: Regardless of the input or any other circumstances, a constant’s fixed numerical value never changes.**Representation:**Constants are frequently represented by**Greek****symbols**or**English****letters**like**pi (π)**and**Euler’s number (e)**or particular**numerical****values**like 2, 7.5, etc.**Immutability**: Constants are immutable; they**retain**their**original value**throughout the course of a calculation or a program.**Use in mathematical formulas**: Fixed values like the speed of light, the gravitational constant, and Planck’s constant are represented by constants in a variety of mathematical formulas.**Application in computer programming**: Constants are used to represent particular values that never change, such as single characters, strings, or special symbols.**Predefined Value**: Constants frequently have**predefined****values**. Examples include mathematical constants like**π**and**e**, as well as physical constants like the speed of light. These numbers have been**calculated**with**great****accuracy**and are**generally****accepted**.

These properties make constants a significant part of any mathematical equation or expression.

**Use of Constants in Daily Life**

Figure 4 – Applications of Constant

Constants are used in a variety of ways in daily life, frequently without our awareness. Here are a few illustrations:

**Timekeeping:**In our daily lives, we measure time using the fixed length of a day. It is simple to**keep****track**of**time**because a day is divided into 24 hours, and each hour is divided into 60 minutes which is constant.**Navigation**: To pinpoint a device’s location, navigation systems like**GPS****use**the**speed**of**light**, a**constant.**In order to pinpoint a device’s location, the GPS system calculates the time it takes for satellite signals to reach the target.**Cooking**: The**temperature****constant**, also known as the**water’s****boiling****point**, is used to calculate the cooking times for various foods. For instance, cooking eggs at a set temperature and time will result in either soft-boiled or hard-boiled eggs.**Physics**: When an object is falling, the velocity and position are calculated using the**constant****acceleration**of**gravity (g).**This is applied in daily life when, for instance, designing roller coasters, figuring out how fast a projectile will travel, or figuring out how tall a building should be.**Engineering**: To calculate the properties of gases, such as pressure, temperature, and volume, engineers use the**gas****constant****(R).**This is crucial when**designing****engines**, engines, and other systems that use gases, such as heating and cooling systems.

There are infinitely many more examples of constants we can observe in daily life.

**Solved Examples Utilizing Constants**

**Example 1**

Consider the equation of line** y = 2x + 2**. Find the **value** of **y** when **x = 2(constant)**.

**Solution**

The equation **y = 2x + 2** **represents** a **line** in this problem, with x serving as the independent variable and y serving as the dependent variable. The **y-intercept** of the **line** is **symbolized** by the **constant** **number** 2, which is used in the equation.

By **substituting** the **value** of **x** into the equation below, we can determine the value of y when** x = 2**.

**y** = 2 (2) + 2

**y** = 4+ 2

**y = 6**

Consequently, **y** **equals** **6** when **x** **equals** **2**.

The **y-intercept** of the line is **represented** in this problem by the **constant** **value** of** 2**, which stays the same throughout the calculation.

**Example 2**

Consider a **scenario** where **Andrew** **went** to **McDonald’s** to **buy** **snacks**. After **3 years**, he again **went** to **McDonald’s** and bought snacks. **Which** **quantity** in this scenario is **constant,** and **which** **quantity** is **variable**?

**Solution**

**Constant**

**McDonald’s** is a **constant** **quantity** in this scenario. At different times, he went to the same shop, i.e., McDonald’s, so that would be a constant.

**Variable**

**Snacks** may be **variable** as he might buy different snacks, and time is also a variable quantity.

*All mathematical drawings and images were created with GeoGebra.*