What is standard form?

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valentin68 | College Teacher | (Level 3) Associate Educator

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There are many standard forms in mathematics. Below are a few examples of such standard forms referring to different things.

1)

If an the equation of a line is referred

`y = m*x +n` where `m` is the slope and `n` the x intercept

its standard form is

`m*x -y =n`  or more general `A*x +B*y =C`

where `A` is positive, and `A, B, C` are the smallest integers that define the line.

2)

If a number is referred, its standard form is the natural way to write it (like for example hundreds digit, followed by tens digit, followed by units digit). Thus for a 4 digit number the expression:

 `2596` is the standard form

whereas `2.596*10^3` is the scientific form.

3)

If you refer to a polinom its standard form is

`P(x) = A_n*X^n +A_(n-1)*X^(n-1)+...+A_0`

beginning with the highest power `n` of `X` (and its coefficient `A_n` ) and continuing with decreasing powers of `X` (`X_(n-1), X^(n-2)...` ) and their corresponding coefficients.

For example a correct standard form for a `4` th degree polinom could be:

`P(X) = 5*X^4 +0*X^3 +2*X^2 +6*X +1`

or simpler: `P(X) =5X^4 +2X^2+6X +1`

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malkaam | Student, Undergraduate | (Level 1) Valedictorian

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Many measurements in modern scientific fields involve very large and very small numbers. For example the speed of light is approximately 300 000 000 m/s, this can be written as follows; speed of light 3.0 * 100 000 000 m/s or 3.0 *10^8 m/s.

The number of significant figures for a particular number becomes definite when it is expressed in this form. Such a number is said to be expressed in the standard form or scientific notation. 

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