What is Standard Form in Mathematics?

What is Standard Form in Mathematics?

A standard form can be defined as a form where one can write a given mathematical concept like an equation, number, or an expression in a form which follows certain rules and terms.

Let us take an example of 4.5 billion years which is written as 4,500,000,000 years.

Writing such large numbers like4.5 billion in its number form is very tedious and time-consuming and there are chances that we may write a few 0’s sometimes more or sometimes less while writing in the number form.

Therefore, to write very large or very small numbers precisely, standard forms are used.

Standard Form Rules

There are certain rules which needs to be followed to write a given mathematical concept like an equation, number, or an expression in the standard form.

The standard form formula varies depending upon the mathematical concept.

For example, the standard form of

Then, what about the fractions  ?

Are there standard forms of fractions?

In the case of standard form of fractions, the numerator and denominator must be co-prime which means that they have no common factor other than 1.

Therefore, the standard form which is also called as the simplest form of the fraction is .

The fraction   is in its simplest form as 13 and 6 are co-prime.

In the above cases, we observed standard forms of writing a decimal number and fractions.

How do we write in Standard Form?

There are various meanings of standard forms depending on which country you are in.

In the United Kingdom and countries using UK conventions, another name for scientific notation is standard form.

In the United States and countries using US conventions, the standard form is a way of writing numbers in decimal notation.

The Standard form = 3890

The Expanded form = 3000 + 800 + 90

The Written form = three thousand eight hundred and ninety

Now let us study the standard form in algebra which includes some major topics like polynomials, linear and quadratic equations.

Standard Form of a Polynomial

Let us consider the algebraic expressions:

Now, let us identify the correlation between all these expressions.

All of the above belong to the family of polynomials. The first two are in their standard form whereas the last two are not.

The rules for writing a polynomial in standard form is very easy.

  • Firstly, the terms have to be written in the descending order of their powers, also called as exponents.
  • Make sure that the polynomial has no like terms.

The standard form is given below:

Standard Form of a Parabola

We all the law of gravity- “what goes up must come down”. This is applicable in standard form of a parabola. Let us see how.

Let us see the shape of a banana and the motion of adolphin in the water.

In both the above cases, they form a simple curve shaped like an arch.

This term is known as a parabola in mathematics.

Thus, a parabola can be defined as the graph of a quadratic function.

The standard form of parabola is given below:

It is to be noted that it has only one squared term.

The following graphs represents two typical parabolas. The intersection of x and y are denoted by green dots, and the vertex of each parabola is marked by a blue dot.

For any quadratic polynomial the graph will have any of the two shapes.

When a > 0, it shows the first parabola (figure 1) which opens upward (u-shaped).

When a< 0, we get a parabola which opens downward (inverted U-shaped) as shown in figure 2.

Now, when y = 0 is put in the above equation, we obtain the x-intercept which is also called as the roots of the equation:

Taking out the roots helps us with the turning point of the parabola.

The vertical line which is drawn from the turning point is known as the axis of symmetry.

Which can be calculated using the formula:

Standard Form of a Linear Equation

The above images are images of lines. Now let us observe the equations of each one of them.

Each has degree 1. That is why, they are called linear equations in two variables.

It can be written in the form:

Therefore, the standard form of linear equation is:

Learn more concepts from the chapter Exponents and Powers from Class 7 Maths

Standard Form of a Line

A linear equation geometrically denotes a line.

Therefore, the standard form of a line is similar to that of a linear equation.

The slope of a given line can be determined for this, the equation for y has to be solved.

For slope, the equation in the form is written as:

y = mx + c

where, m represents the slope of the line.

The standard form of slope is given below:

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