Standard form in mathematics is a way of writing numbers, equations, or expressions in a consistent and simplified format that makes them easier to understand, compare, and work with. Specifically, for numbers, standard form (also known as scientific notation) expresses a number as the product of two parts:

• A decimal number aaa such that 1≤a<101\leq a<101≤a<10
• Multiplied by a power of 10, written as 10n10^n10n, where nnn is an integer

For example, the number 420 can be written in standard form as 4.2×1024.2\times 10^24.2×102

. In the context of equations, such as quadratic or polynomial equations, standard form means writing the terms in descending order of their degree (highest power first), which helps clearly identify coefficients and understand the equation's behavior. For example, the polynomial 3x4−2x3+5x2−7x+13x^4-2x^3+5x^2-7x+13x4−2x3+5x2−7x+1 is in standard form

. Standard form is widely used for very large or very small numbers, such as distances in astronomy or sizes of microscopic particles, because it simplifies reading and calculations

. In summary, standard form is a standardized way to write mathematical elements-most commonly numbers-as a decimal between 1 and 10 multiplied by a power of 10, facilitating clarity and ease of use in mathematical operations