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 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
Also, within each term, it is nice to have the variables in alphabetical order (if it does not make things more confusing):
Example: Put this in Standard Form:
yzx2 + 4yx3
The highest degree is 3, so that goes first, also put the variables in alphabetical order
4x3y + 3x2yz
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 of a Circle Equation
With a circle like this:
The Standard Form is this:
(x−a)2 + (y−b)2 = r2
See Circle Equations for more details.