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:

5326.6 = 5.3266 times 10 to the 3
In this example, 5326.6 is written as 5.3266 × 103,
because 5326.6 = 5.3266 × 1000 = 5.3266 × 103

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

561 500 + 60 + 1
Standard Form Expanded Form

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

ax² + bx + c = 0

(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