Scientific Notation

N × 10^n with 1 ≤ N < 10: the standard compact form for the very large and very small numbers chemistry runs on.

a \times 10^n, \quad 1 \le a < 10

a x 10^n, where 1 <= a < 10

What it means

Scientific notation splits any number into a small coefficient and a power of ten that sets its scale. Move the decimal point left and the exponent is positive (big numbers like Avogadro's number, 6.022 × 10²³); move it right and the exponent is negative (tiny numbers like an atomic radius, 1.0 × 10⁻¹⁰ m). It keeps calculations readable, makes orders of magnitude obvious at a glance, and carries significant figures cleanly.

Variables

Symbol	Name	Unit	Meaning
$a$	Coefficient	dimensionless	The coefficient, kept between 1 and 10 so the scale is carried entirely by the exponent.
$n$	Exponent	dimensionless	The integer power of ten; positive for large numbers, negative for small ones.
$10$	Base	dimensionless	The base, fixed at 10 in scientific notation.

Assumptions

The coefficient a stays between 1 and 10 (10 itself is written as 1 × 10¹).
The exponent n is an integer counting decimal-place moves.
Significant figures live in the coefficient, never in the power of ten.
A positive exponent means a large number; a negative exponent means a small one.

Worked example

Problem

Write 452,300 in proper scientific notation.

Given:

Number to convert: 452,300

Place the decimal after the first nonzero digit: 4.52300.
Count how many places it moved left: 5.
Moving left means a positive exponent: n = +5.
Assemble: 452,300 = 4.523 × 10⁵.
Verify: 4.523 × 100,000 = 452,300.

4.523 × 10⁵

The 10⁵ immediately shows this is a hundred-thousands-scale number, while the coefficient keeps all four significant figures intact.