# Standard Form

Last Updated: August 21, 2024

## Standard Form

In mathematics, there are complex structures of equations that can come in a variety of forms. The standard form is the most used format of a specific equation or numerical notation.

## What Is Standard Form

The standard form is a modifier used in math to describe the basic format of a specific equation. Examples of the standard form include the standard form of a differential equation, the standard form of a linear equation, and the standard form of the indices. There is also another type of standard form outside of math, like a standard form certification and a standard form for medication.

## How to Solve the Standard Form of a Quadratic Equation

The standard form of the quadratic equation will appear as ax2 + bx + c = 0. Where x is the unknown values and a, b, and c are the known values. The quadratic equation is used to search for the curve of a specific action, or object.

### 1.) Write Down the Equation

Begin by writing down the equation on a piece of paper or digital note-taking software. This will help you visualize the overall equation of the standard form of a quadratic equation.

### 2.) Move all Numbers and Variables to the Left-Side of the Equation

After writing the equation down, substitute each variable and move all numbers and variables to the left side of the equation. We do this to easily apply the quadratic formula to the quadratic equation.

### 3.) Simplify the Expression

If possible, you must simplify the expression with its lowest common denominator or LCD. This will help make the values in the expression easier to work with.

### 4.) Apply the Quadratic Formula and Solve the Equation

After simplifying the expression and moving all the numbers and variables to the left side of the expression, you will now apply the quadratic formula to solve the equation. This formula will come in the form of x = ?b ± ?(b2 ? 4ac)/2a. The same values apply for the quadratic equation (ax + by + c), meaning that the a in the quadratic equation is the same a used in the quadratic formula.

### 5.) Solve the Quadratic Formula

Solve the quadratic formula to find the value of X. Be sure to follow the order of operations and begin with the exponents and multiplication inside the parentheses. Avoid applying the ?b ± part of the formula as this will be followed through at the next step.

### 6.) Solve for Two Values of X

After you have solved the quadratic formula you must find the two values of X. To do this you must solve both the plus and the minus side of the -b. When you have finished doing this, you will end up with two values of X.

## What is the standard form of a decimal?

The standard form of a decimal follows the format of X.Y, where X is the whole number and Y is the decimal number. An example of this is 2.15 where 2 is the whole number while 15 is the decimal. But if we are referring to the standard form as a British term then we will refer to scientific notation. People characterize standard notation by a specific format of X × 10Y where X is the rational number and Y is the exponent, Y is the number of times the decimal point moves, and the symbol of Y denotes the direction the decimal moves. When writing a standard notation in word form the format should be “X multiplied in the power of Y.” People use the standard notation to express numbers whose values are exponentially large or small. An example of the usage of standard notation would be the shortening of 15 000 000 to 15 x 106,

## Standard vs. Expanded form; what is the difference between standard and expanded form?

Standard form is the expression of a number as the person has written it. This means that when someone writes a number as five hundred sixty-five, you will convert this written number to standard form as 565. While expanded form is the expression of the number as a summation of all its values. Following the example above five hundred sixty-five will be written as 500 + 60 + 5 in expanded form. Though we usually use the standard form in our expression of numbers the expanded form has some niche uses.

## Can irrational numbers be written in standard form?

Yes, you can express irrational numbers in standard form, with some exceptions and modifications. If we were to express ? in standard form, then it will span the whole page to infinity. But if we were to express ? to a certain degree in decimal places then we would be able to express the irrational number in standard form. For example, if someone asks you to express ? to the 6th decimal place then we will write it down as 3.141593. If you wish to express an infinite value then you may use … to express that the number reaches infinity. Using the above example, you will express ? as 3.1615926…

People have defined standard form as the most basic form of a numerical expression. When used correctly standard form can communicate the number you want to express to the person.

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