Standard Form Worksheet, Definition, and Examples

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How to Go from Scientific Notation to Standard Form (Step by Step) | 8th Grade

Key Points about Standard Form

  • Standard form is a format used to express linear equations in two variables.
  • To convert an equation to standard form, one needs to manipulate the equation by adding or subtracting terms until it is in the form Ax + By = C.
  • Standard form is widely used in algebra and is an essential concept to understand for students who want to excel in math.

Standard Form for Scientific Notation

In order to Convert Numbers from Scientific Notation you move the decimal point based on the exponent on the power of ten. The exponent on the power of ten tells you the number of spaces you must move the decimal point. If the exponent is positive, the decimal moves to the right. If the exponent is negative, the decimal moves to the left. When you Convert Numbers from Scientific Notation you will have either a decimal or a large whole number as an answer. If the exponent is negative then you will have a decimal as an answer. If the exponent is positive, then you will have a large whole number as an answer.

Standard form is a commonly used format in mathematics to express linear equations in two variables. It is a format that makes it easy to find both the x and y intercepts of a line. In standard form, the equation is written as Ax + By = C, where A, B, and C are integers and A is non-negative.

To convert an equation to standard form, one needs to manipulate the equation by adding or subtracting terms until it is in the form Ax + By = C. This format is preferred because it is easier to graph and compare equations, and it provides a clear view of the relationship between the variables.

Standard form is widely used in algebra and is an essential concept to understand for students who want to excel in math. In this article, we will explore the definition of standard form, how to convert equations to standard form, and provide some examples of standard form equations. We will also answer some frequently asked questions about standard form to help readers better understand this important concept.

Common Core Standard: 8.EE.A.3
Basic Topics:
Related Topics: Square Roots, Cube Roots, Irrational Numbers, Powers of 10, Scientific Notation Intro, Converting Numbers to Scientific Notation, Converting Numbers from Scientific Notation, Adding and Subtracting in Scientific Notation, Multiplying in Scientific Notation, Dividing in Scientific Notation
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Example of Standard Form

Standard Form Definition in Math

In math, standard form is a common way of representing a mathematical element. It can refer to the way numbers, fractions, equations, or expressions are written down. Standard form is a general term that means “written down in the way most commonly accepted.”

For numbers, standard form can refer to scientific notation or expanded form. In scientific notation, a decimal number is written as a power of 10 multiplied by a decimal between 1 and 10. For example, the number 3,450,000 can be written in scientific notation as 3.45 x 10^6. In expanded form, a decimal number is written as the sum of its digits multiplied by the appropriate power of 10. For example, the number 125 can be written in expanded form as 100 + 20 + 5.

For equations, standard form can refer to the form Ax + By = C, where A, B, and C are constants. This form is useful because it allows the x- and y-intercepts of the line to be easily found by setting x or y equal to 0 and solving for the desired variable.

In fractions, standard form refers to writing the fraction with the numerator and denominator in their simplest form. For example, the fraction 4/8 can be written in standard form as 1/2.

Overall, standard form is a way of representing mathematical elements in a clear and concise manner. It allows for easy comparison and manipulation of different elements. When working with mathematical expressions, it is important to understand standard form and how to convert between different forms when necessary.

 

Convert to Standard Form

When working with linear equations, it is often useful to convert them to standard form, which is in the form of Ax + By = C. This section will cover how to convert numbers to standard form from scientific notation and decimal form.

From Scientific Notation

To convert a number from scientific notation to standard form, you need to use the power of 10. The general form of a number in scientific notation is a x 10^b, where a is a decimal number between 1 and 10, and b is an integer. To convert this to standard form, you need to multiply a by 10^b and then write it in the form of Ax + By = C.

For example, to convert 3.45 x 10^6 to standard form, you would first multiply 3.45 by 10^6 to get 3,450,000. Then, you can write this in the form of Ax + By = C by choosing any two coefficients for x and y. For instance, you can choose A = 10 and B = 100 to get 10x + 100y = 3,450,000.

From Decimal

To convert a decimal number to standard form, you need to move the decimal point until there is only one non-zero digit to the left of the decimal point. Then, you need to use the power of 10 to write it in the form of Ax + By = C.

For example, to convert 0.000345 to standard form, you would move the decimal point six places to the right to get 345. Then, you can write this in the form of Ax + By = C by choosing any two coefficients for x and y. For instance, you can choose A = 1000 and B = 100 to get 1000x + 100y = 345.

In summary, converting to standard form can be done from both scientific notation and decimal form. By following the steps outlined above, you can easily convert any number to standard form, which can be useful when working with linear equations.

Example of Standard Form Solution

3 Simple Standard Form Examples

  1. To convert a number to standard form, you have to move the decimal according to the exponent of the power of ten.
  2. The number of the exponent tells you how many times the decimal will move.
  3. If the exponent is negative, the decimal moves left.
  4. If the exponent is positive, the decimal moves right.

Standard form is a way of writing numbers and equations that makes them easier to read and work with. In this section, we will explore some examples of how standard form is used in linear equations.

Linear Equations

A linear equation is an equation that describes a straight line. Standard form for linear equations is written as Ax + By = C, where A, B, and C are constants and x and y are variables. This form is useful because it allows you to quickly identify the slope and y-intercept of the line.

Here are some examples of linear equations in standard form:

  • 2x + 3y = 6
  • 4x - 5y = 20
  • x - y = 3

Slope-Intercept Form

Slope-intercept form is another way of writing linear equations. It is written as y = mx + b, where m is the slope of the line and b is the y-intercept. This form is useful because it makes it easy to graph a line and find its slope and y-intercept.

Here are some examples of linear equations in slope-intercept form:

  • y = 2x + 3
  • y = -3x + 2
  • y = 0.5x - 1

Point-Slope Form

Point-slope form is another way of writing linear equations. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. This form is useful when you know the slope of a line and a point on the line, but not the y-intercept.

Here are some examples of linear equations in point-slope form:

  • y - 5 = 2(x - 3)
  • y + 2 = -0.5(x - 4)
  • y - 1 = 3(x + 2)

By using standard form, slope-intercept form, and point-slope form, you can write and work with linear equations in a variety of ways.

 

5 Quick Standard Form Practice Problems

/5

Converting from Scientific Notation to Standard Form

Click Start to begin the practice quiz!

1 / 5

Convert the following to Standard Form:

5.2 x 10^5

2 / 5

Convert the following to Standard Form:

6.45 x 10^-4

3 / 5

Convert the following to Standard Form:

4.7 x 10^-3

4 / 5

Convert the following to Standard Form:

3.4 x 10^4

5 / 5

Convert the following to Standard Form:

7.8 x 10^3

Your score is

0%

 

Standard Form Formula

The standard form formula is a commonly accepted way of representing mathematical concepts like equations, expressions, and numbers. This formula follows certain rules or formulas that vary depending on the mathematical concept being represented.

Standard Form of a Linear Equation

The standard form of a linear equation in two variables is given by the equation: Ax + By = C, where A, B, and C are constants. This form is useful because the x- and y-intercepts of the line can be easily found by setting x or y equal to 0, then solving for the desired variable.

Standard Form of a Polynomial

The standard form of a polynomial is to write the terms with a higher degree first (descending order of degree) and its coefficients must be in integral form. For example, consider the polynomial 3x^2 – 7 + 4x^3 + x^6. The highest degree is 6, so that goes first, then 3, 2, and then the constant last: x^6 + 4x^3 + 3x^2 – 7.

Standard Form of a Number

The standard form of a number is a way of writing very large or very small numbers in a concise and easy-to-read format.

 

Converting to Standard Form FAQ

How do I convert a linear equation to standard form?

To convert a linear equation to standard form, you need to rearrange the equation so that it is in the form Ax + By = C, where A, B, and C are integers and A is positive. This can be done by moving all the variables to the left-hand side of the equation and all the constants to the right-hand side.

What are the rules for writing a number in standard form?

To write a number in standard form, you need to express it as a number between 1 and 10 multiplied by a power of 10. For example, the number 3,450,000 can be written in standard form as 3.45 x 10^6. The exponent of the power of 10 represents the number of places the decimal point needs to be moved to get the original number.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to zero. This form makes it easy to identify the coefficients of the equation and to use the quadratic formula to solve for the roots of the equation.

How do I write a large number in standard form?

To write a large number in standard form, you need to express it as a number between 1 and 10 multiplied by a power of 10. The exponent of the power of 10 represents the number of digits in the original number. For example, the number 123,456,789 can be written in standard form as 1.23456789 x 10^8.

What is the standard form formula?

There is no single standard form formula. The term “standard form” can refer to different forms depending on the context. For example, in algebra, standard form refers to the form Ax + By = C for a linear equation, while in math, standard form refers to the form a x 10^n for a number.

What is the relationship between slope and standard form?

In the standard form of a linear equation, Ax + By = C, the slope of the line is given by -A/B. This means that lines with the same slope have the same ratio of A to B in their standard form equations.

What is an example of standard form notation?

An example of standard form notation is the equation 2x + 3y = 6, which is in the standard form Ax + By = C for a linear equation. Another example is the number 0.000000000000000000000000000000000001, which can be written in standard form as 1 x 10^-36.

 

Scientific Notation to Standard Form Worksheet Video Explanation

Watch our free video on how to solve Standard Form. This video shows how to solve problems that are on our free Example of Standard Form worksheet that you can get by submitting your email above.

Watch the free Standard Form video on YouTube here: Example of Standard Form

Video Transcript:

This video is about converting numbers from scientific notation into standard form example. You can get the scientific notation to standard form worksheet we use in this video for free by clicking on the link in the description below.

The directions for our practice problems say to convert the following numbers from scientific notation into standard form. Jumping down to the first problem about standard form examples it gives us 9 times 10 to the third power. We have to convert this number from scientific notation into standard form. Every number written in scientific notation has a coefficient times a power of 10. The power of 10 tells you how many times you have to move the decimal point. This exponent in particular tells you how many times the decimal point moves either to the left or to the right. If this exponent is positive, it will move the decimal point to the right and if this exponent is negative, it will move the decimal point to the left.

Let’s go ahead and complete this first problem on the scientific notation to standard notation worksheet. Once again the first problem is 9 times 10 to the third power it asks to convert to standard form. We already know that the decimal is located right here after the 9 because this 9 is our coefficient so we’re going to rewrite the 9 with a decimal point after it. Now this power of 10 here, 10 to the third power, has an exponent of 3.

That 3 is positive so that means you’re going to move the decimal three spots to the right. We will take our decimal place here and we will move it one, two, three times to the right and we will add our new decimal. Everywhere there is an empty space we’re going to add a zero for the placeholder. To simplify 9 times 10 to the third would be nine thousand in standard form so our answer is nine thousand and that’s how you convert standard form to scientific notation.

Number two gives us five point zero one times ten to the negative fourth and is the second examples of standard form. Now we already know where our decimal is located because it’s given to us in the problem so let’s go ahead and rewrite our coefficient as five point zero one the power of ten. This time we an exponent of negative four. This four means we’re going to move the decimal four times and because it’s negative that means we move the decimal four times to the left. We’ll take our decimal and we’ll go one, two, three, four times to the left and we will put our new decimal point. And then everywhere there’s an empty space we will add a zero. Our solution from scientific notation in standard form is point zero zero zero five zero one and that’s going to be our answer.

The last problem we’re going to convert from scientific notation into standard form is number ten. Number ten gives us one point zero zero zero three five times 10 to the fourth power and is another example of standard notation. We already know where our decimal is because it’s included in the coefficient. We’ll write one point zero zero zero three five under our problem. Our power of 10 has an exponent of four. We know we have to move it four times and the 4 this time is positive so we will move the decimal point to the right because the 4 is positive.

We take our decimal point and we go one, two, three, four times to the right and we will add our new decimal point. Then we’re going to rewrite this in standard form. It will be one zero zero zero three point five or ten thousand and three point five and that’s going to be our answer. Try all the practice problems by downloading the free converting to and from standard form worksheet above.

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