Scientific notation is a way of expressing very large or very small numbers in a compact form. It is written as the product of a number (called the significand or mantissa) and a power of ten. The general form is:
\[ N = a \times 10^n \]
where:
- \( a \) is a number greater than or equal to 1 and less than 10 (the significand), and
- \( n \) is an integer (the exponent) that indicates how many places the decimal point has been moved.
For example:
- The number 300,000 can be expressed in scientific notation as \( 3.0 \times 10^5 \).
- The number 0.0045 can be expressed as \( 4.5 \times 10^{-3} \).
Scientific notation is widely used in scientific, engineering, and mathematical contexts to simplify computations and to easily handle very large or very small values.