Which equation is written in standard form?

What is "Standard Form"?

that depends on what you are dealing with!

I have gathered some common "Standard Form"s here for you..

Note: Standard Form is not the "correct form", just a handy agreed-upon style. You may find some other form to be more useful.

Standard Form of a Decimal Number

In Britain this is another name for Scientific Notation, where you write down a number this way:

In other countries it means "not in expanded form" (see Composing and Decomposing Numbers):

Standard Form of an Equation

The "Standard Form" of an equation is:

(some expression) = 0

In other words, "= 0" is on the right, and everything else is on the left.

Example: Put x2 = 7 into Standard Form

Answer:

x2 − 7 = 0

Standard Form of a Polynomial

The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first (like the "2" in x2 if there is one variable).

Example: Put this in Standard Form:

3x2 − 7 + 4x3 + x6

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x6 + 4x3 + 3x2 − 7

Standard Form of a Linear Equation

The "Standard Form" for writing down a Linear Equation is

Ax + By = C

A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

Example: Put this in Standard Form:

y = 3x + 2

Bring 3x to the left:

−3x + y = 2

Multiply all by −1:

3x − y = −2

Note: A = 3, B = −1, C = −2

This form:

Ax + By + C = 0

is sometimes called "Standard Form", but is more properly called the "General Form".

Standard Form of a Quadratic Equation

The "Standard Form" for writing down a Quadratic Equation is

(a not equal to zero)

Example: Put this in Standard Form:

x(x−1) = 3

Expand "x(x-1)":

x2 − x = 3

Bring 3 to left:

x2 − x − 3 = 0

Note: a = 1, b = −1, c = −3

Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form.

Small numbers can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative. The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10(to the power of a number).

This video explains standard form:

Example

Write 81 900 000 000 000 in standard form: 81 900 000 000 000 = 8.19 × 1013

It’s 1013 because the decimal point has been moved 13 places to the left to get the number to be 8.19

Example

Write 0.000 001 2 in standard form:

0.000 001 2 = 1.2 × 10-6

It’s 10-6 because the decimal point has been moved 6 places to the right to get the number to be 1.2

On a calculator, you usually enter a number in standard form as follows: Type in the first number (the one between 1 and 10). Press EXP . Type in the power to which the 10 is risen.

Manipulation in Standard Form

This is best explained with an example:

Example

The number p written in standard form is 8 × 105

The number q written in standard form is 5 × 10-2

Calculate p × q. Give your answer in standard form.

Multiply the two first bits of the numbers together and the two second bits together:

8 × 5 × 105 × 10-2

= 40 × 103 (Remember 105 × 10-2 = 103)

The question asks for the answer in standard form, but this is not standard form because the first part (the 40) should be a number between 1 and 10.

= 4 × 104

Example

Calculate p ÷ q.

Give your answer in standard form.

This time, divide the two first bits of the standard forms. Divide the two second bits. (8 ÷ 5) × (105 ÷ 10-2) = 1.6 × 107

What is standard form give example?

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What are standard forms?