Standard form is a way of writing down very large or very small numbers easily. While writing a number in standard form, write down a number between 1-10 then you write "$\times$ 10" (to the power of a number).

For large numbers the index will be positive where as for small numbers the index will be negative.

## How to Write Standard Form?

In mathematics standard form is written by breaking down the number into segment of tens, hundreds etc., An addition (+) symbol is used in between numbers to make the equation true. It is written in numbers as opposed to being written in words. Should be written exactly as in number digits.

For example: 3275 is written as 3000 + 200 + 70 + 5.
3275 = 3275

## Standard Form Equation

Standard form of an equation is:
(Some Expression) = 0.

### Solved Example

Question: Put $x^{3}$ - $2x^{2}$ - 7x = 5 into standard form.
Solution:

$x^{3}$ - $2x^{2}$ - 7x - 5 =0

## Algebra Standard Form

To represent complex equations in simple form we use standard form of algebra. There are different equations in algebra which can be slope intercept form, linear equations, quadratic equations, exponential equations, radical equations etc.,
The standard form of an linear equation is Ax + By + C =0For example, the equation y = 2x - 6 is in Slope Intercept form
In standard form it can be written as 2x - y = 6

Using the given quadratic equation we can easily find the factors which will be in the simplest form.

## Polynomial Standard Form

A polynomial is an expression consisting variables, constants and positive integer exponents of the variables. A polynomial is said to be in standard form when its highest powers of an given equation is in order.
Highest degree - First
Second highest degree - Second
Third highest degree - Third and so on.

Example: $2y^{4} + y^{3}$ + 7y + 2 is in polynomial standard form.

## Examples of Standard Form

### Solved Examples

Question 1: Write 0.000000089 in standard form
Solution:

0.000000089 = $8.9 \times 10^{-8}$

It is $10^{-8}$ because the decimal is been moved 8 places to the right to get 8.9.

Question 2: Put x (x - 1) = 3 in standard form.
Solution:

Expanding x(x - 1) = 3 we get,

$x^{2}$ - x = 3

Bring 3 on the left hand side
$x^{2}$ - x - 3 =0
Therefore,  $x^{2}$ - x - 3 = 0  is in the standard form.