In math, the definition of standard form can be different, depending on whether one means the standard form of a large number or the standard form of different equations. If standard form is in relationship to expressing small or large numbers, then it means using scientific notation. However, when it is in relationship to an equation, it can have different meanings.
In terms of standard form of a large number like 5,100,000, one can express this in scientific notation as 5.1 multiplied by 10 raised to the sixth power, or 5.1 x 10^6. When one has a small or decimal number like 0.0000051, one can express this as 5.1 multiplied by 10 to the negative sixth power, or 5.1 x 10^-6.
If one uses the term standard form in connection to equations, then it can mean the correct way to write a simple equation, a line equation, quadratic equation or a polynomial equation.
In math, if one sees an equation like x squared equals 24, or x^2 =24, then the standard form for it is to write it as x^2 - 24 =0. This means that one must place variables and number to the left of zero for it to be in correct standard form.
Similarly, the standard form for a line equation is Ax + By = C, where A, B and C represent integers. If a line equation is not in this form, then one has to rearrange it into this form. Likewise, the standard form to express a polynomial is to place terms of the equation from ascending to descending degrees, such as x^6 + x^3 + 2x^2 -16. For quadratic equations, the standard form is Ax^2 + Bx + C =0.