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What is a constant in math?

Literally speaking, constant means non-changing. Similarly, in mathematics constant refers to an expression or an object that does not change its value irrespective of its usage.

On the other hand, a variable means whose value can change.

For example, refer to this polynomial

5{{r}^{2}}+4r+9

Here, r is the variable, 5 & 4 and 9 are known as constants. 9 is also known as the constant term in this polynomial. We can also say that coefficients of polynomial where the variable is raised to power zero are constants.

This means that the 9 will remain constant irrespective of the value of r. It has no dependency and has independent existence.

We can also say that, all constants are definable and computable numbers.

Constants are everywhere

The value of a constant is fixed. Apart from numbers, there are many other derived constants that were invented by many renowned mathematicians such as e,\pi

Let’s discuss the same with a few examples:

  • In the expression 8h + 6, 8 and 6 both are constants and are also known as coefficients of {{h}^{1}} and {{h}^{0}}  .
  • In the expression 8b, 8 is the constant.
  • -8xy, here -8 is the constant.

Let’s take some real-life examples:

  • The number of months in a year i.e. 12 is a constant.
  • We have two eyes and 10 fingers. This number can never be changed.

To clear out the confusion let’s draw differences between Constants and Variables

 

  Variables Constants
1. The value of a variable changes depending on its usage. The value of constant remains fixed. It cannot be altered.
2. These are represented by letters of alphabets and are usually written in lowercases. The value of a constant is always a number be it natural, integer fraction, rational or irrational number.
3. A variable’s value is always unknown. The value is always known.
4. For example: x, y, a,b, sin θ etc For example:  4, 5, 1.6,

 

Notable mathematical constants

Apart from numbers that we know, there are some mathematical constants that are either derived or invented by famous scientists and mathematicians. These objects are called mathematical constants. These are:

  • πor pi, This symbol denotes that the ratio of a circle’s circumference to the diameter of the circle always comes out be 3.141592653
  • i , or the imaginary part of the complex number (a+ib) is always equal to  or  \sqrt{{-1\,or\,{{i}^{2}}\,=\,1.}}
  • The value of (Euler’s number) is approx. 2.718281828…
  • Zero
  • One (1), the successor of zero
  • Pythagoras constant or \sqrt{2} is equal to 1.414.

Let’s practice this with some examples:

Problem 1:  Find the constant terms in 4x+3\,=\,9y-10

For that we need to first simplify the equation:

4x-9y\,=\,-10-3; 4x-9y\,=\,\,-13

The constant term is -13.

4x &  -9y are variable terms.

Problem 2: Harry has 5 apples and Thea has 12 apples more than Benjamin. Find the constants and variables in this scenario?

Let’s understand how many apples each has:

Harry has 5 apples.

Say, Benjamin has  apples

So, Thea has x+12 apples.

The only constant here is 5, as the number of apples owned by Thea and Benjamin depend on variable .

 

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