Scientific notation
Definition
A compact way to write very big or very small numbers as a number between 1 and 10 times a power of 10 — like writing 6,000,000,000 as 6 × 10^9.
Technical definition
Representation of a number as a × 10^b, where 1 ≤ |a| < 10 and b is an integer. It makes the order of magnitude explicit and simplifies multiplication and division of extreme values.
Example
The speed of light is 299,792,458 m/s — far easier to read and use as 2.99792458 × 10^8 m/s. Multiplying (2 × 10^3)(3 × 10^4) is just 6 × 10^7: multiply the fronts, add the exponents.
The exponent counts how many places the decimal point moved, and its sign matters: large numbers get positive exponents, small numbers get negative ones. Writing 0.0005 as 5 × 10^3 (instead of 5 × 10^-4) is the most common slip — always check which way the point moved.