powerof10

Power of ten, or powers of ten, refers to numbers of the form 10^n where n is an integer. Positive exponents yield 10, 100, 1000, and so on, while zero yields 1, and negative exponents yield fractions such as 0.1 or 0.001. Powers of ten provide a simple scaling system in decimal arithmetic and underpin scientific notation, in which a number is written as a × 10^n with a between 1 and 10.

They are used to express orders of magnitude, allowing concise representation of very large or very small quantities. Examples include Avogadro’s number, approximately 6.022×10^23, the speed of light, about 3.0×10^8, and measurement uncertainties expressed as a small power of ten, such as 2×10^-3.

In the International System of Units (SI), many prefixes denote powers of ten: kilo 10^3, mega 10^6, giga 10^9, tera 10^12, peta 10^15, exa 10^18, and so forth, with corresponding milli 10^-3, micro 10^-6, nano 10^-9, pico 10^-12, etc. These prefixes enable convenient expression of quantities across science, engineering, and everyday life.

In mathematics, powers of ten relate to the logarithm base 10, with log10(10^n) = n and 10^(log10 x) = x for x > 0. Powers of ten underpin the metric system, scientific notation, and many methods of measurement, calculation, and data presentation.