Standard Form

Standard form is generally a syntax kind for expressing mathematical operations. Learn about the concept here or you can also connect to an online tutor anytime and thus gain your answers to math problems regarding standard form. Get your help now. Below is explained about standard form in math, algebra and equations.

The definition of Standard form is that it is a way of writing down very large or very small numbers easily. 10³ = 1000, so 4 x 10³ = 4000. So 4000 can be written as 4 × 10³. Standard form is also used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form.

Example: Write 50 400 000 000 000 in standard form: 50 400 000 000 000 = 5.04 × 10¹³

It’s 10¹³ because the decimal point has been moved 13 places to the left to get the number to be 5.04

Standard form algebra is used to write down the complex equations in a simple form i.e. to write a large equation very easily. For example standard form of a linear equations is ax + by + c= 0, standard form of quadratic equation is ax² + bx + c = 0. Standard form algebra is used to find out the factors. Example:

3x² + 11x - 4 = 0 [3 x 4 = 12]

12 - 1 = 11(since 11 is b)

3x² + 12x - x - 4 = 0

3x (x + 4) -1 (x + 4)

So the factors are (3x - 1) and (x + 4).

xy + 3y - 2x - 6 = 0

arrange them in an order now.

We get xy - 2x + 3y - 6 = 0

x (y - 2) + 3 (y - 2) = 0

(x + 3) (y - 2) = 0

So here (x + 3) and ( y - 2) are the factors.

Standard form equation is the general representation of an equation. There are different types of standard form equation such that linear equation, quadratic equation, polynomials etc. Example:

Find the equation of a line if slope is 2 and passing through a point (2, 4)

Given that

Slope m = 2 Point = (2, 4)

Equation of a line passing through a point and with slope m is y - y₀ = m (x - x₀)

y - y₀ = m (x - x₀)

y - 4 = 2 (x - 2)

y - 4 = 2x - 4

2x - 4 - y + 4 =0

2x - y - 4 + 4 =0

2x - y =0

Therefore equation of a line is 2x - y = 0.