A standard form is an important way in mathematics that allows us to signify numbers and equations in a standardized format. This makes it easier to compare and manipulate large or small numbers and perform operations on equations, circles, lines, and polynomials.

Whether you are working with linear equations, quadratic equations, and polynomials of a higher degree, understanding standard form is essential for success in mathematics. This article will explore the standard form, its applications, examples, and equations.

## Definition of Standard Form

The way of writing numbers always includes a decimal point and a power of 10. It is denoted by **A*10 ^{n}** in this form the

**n**must be an integer where

**A**is between 1 to 10. It is used for many other terms like line circles, numbers, etc.

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To clarify the concept of standard form we will discuss various formats

### The standard form of numbers:

For writing numbers in standard form, you need to move the decimal point to the right or left until the number is between 1 and 10. Let us use an example to help comprehend the standard form of numbers.

**Example 1: (for numbers in standard form)**

Show the given number in standard form 35,000,00

**Solution:**

The standard form of a number can be obtained with the help of a standard notation calculator. Below steps will help you to find the standard form manually.

**Step 1:**

First, we move the decimal point left or right until I get the number between 1 and 10 so,

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3.5,000,00 we move the decimal point to the left and 3.5 is the number between 1 and 10 so according to the denoted formula our **A **is 3.5

**Step 2:**

Now we count the number of times we moved the decimal point to the left so we moved the decimal point 6 times this means our **n** is 6

**Step 3:**

A standardized form of this number is 3.5 *10^{6}

**Note:**

- if we moved the decimal to the left this indicates that the power is positive
- if we moved the decimal to the right this indicates that the power is negative

### The linear equation in standard form:

The linear equation in standard form is Ax + By = c (x, y are variables)

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The coefficient and constants A, B, and C must be real numbers and the coefficient (A, B) not be zero.

If the equation is given in the line intercept form (y = mx + b) and you want to convert in the standard form you must get the variables on the same side of the equal and constant c on the other side of the equal

**Example 2: (for linear equation)**

Write the below linear equation in standard form

Y = -7x + 10

**Solution:**

The given equation in the line intercept form so,

**Step 1:**

Re-arranging the equation

Y + 7x = 10 so x is the leading term we rewrite the equation like this,

The standard form of the given equation is 7x + y = 10.

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### The circle in standard form:

This type of equation is the standard form of the circle (x – h)^{2} + (x – k)^{2} = r^{2} where **h and k** are constants and **r** is the radius. let’s try to grasp the standard form of the circle by using an example

**Example 1:**

Express the given equation in standard form when the center (10,6 ) and radius are 3

**Solution:**

**Step 1:**

The standard equation of the circle is,

(x – h)^{2} + (y – k)^{2} = r^{2} so in the given points the

h = 10 and k = 6 where radius 3

**Step 2:**

By putting values in a given equation we get

(x – 10)^{2} + (y – 6)^{2} = 3^{2}

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The equation represents all the points on the plane that are 5 units away from the center and makes the circle with center 5,7

### The fraction in standard form:

A fraction in standard form is a way of writing a number in which both the numerator and denominator are co-prime numbers (the numbers which have only common divisor 1) for example 2, 3, 5, 7, and 11 all are co-prime numbers.

Trying to comprehend through the example could be useful, 5 / 3, 7 / 11, and 13 / 2 all are standard fractions. Now the question arises here if the fraction is not in the standard form how do we convert it into standard form?

Don’t worry we will learn this also

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**Conversion of fraction into the standard form:**

Let us have a fraction of 12 / 16 now this fraction is not in standard form so we convert it into standard form step by step

- First of all, we find the all-common divisor of this fraction the divisor of 12 is 1, 2, 3, 4, 6, and 12 and the fraction of 16 is 1, 2, 4, 8, and 16
- Divide the fraction with gcd (greatest common divisor) 4
- Now the fraction is 3 / 4 this is the standard form of 12 / 16

## Applications of the standard form:

Standard form is used in many fields including science, physics, engineering, finance

- Standard form is used in physics for the mass of very small sub-atomic particles
- Standard form is used in engineering for the resistance of electrical components which can be very large or small
- Standard form is used in finance for the witting of a large amount of money such as national debt in the country

## Summary:

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In this article, we have tried to cover the basic concept of standard form with the assistance of definitions and examples and also discussed the standard form of different terms like circles, polynomial linear equations, and fractions. In the last section, we learned some applications of the standard form.

I hope that after reading this article, you will be able to handle all the queries related to the term “standard form”