exponentnotation

Exponent notation is a compact way to represent numbers using a base raised to an exponent, commonly used to express very large or very small values. In its most familiar form, scientific notation expresses a number as a significand (a decimal number usually between 1 and 10) multiplied by 10 raised to an integer exponent, for example 3.2 × 10^5 to represent 320,000. Variants include engineering notation, which restricts the exponent to multiples of three, and "E notation" used in computing (e.g., 3.2E5).

The notation highlights magnitude and significant figures, making it useful in scientific, engineering, and financial contexts where precision and scale must be conveyed simultaneously. Arithmetic with exponent notation follows rules of exponents: multiplying or dividing numbers adjusts exponents directly, while addition and subtraction require aligning exponents before combining significands.

Exponent notation is not limited to base 10; mathematicians often use other bases (such as base 2 in computer science), and exponents can be non-integer in more advanced contexts. In computing, floating-point formats like IEEE 754 store numbers roughly in sign–significand–exponent form, enabling a wide dynamic range but introducing rounding and representation limits.

The notation streamlines communication of measurements and calculations, standardizes presentation across disciplines, and eases display on limited-space devices, while also requiring awareness of rounding, normalization conventions, and domain-specific formatting.