Powers of ten

Powers of ten are numbers of the form 10ⁿ, where n is an integer. They encode decimal place values and provide convenient factors for expressing scale.

Exponentiation: Repeated multiplication, extended to define powers with zero, negative, and fractional exponents. Powers of ten are a special case of exponentiation.
Exponent laws: Rules governing products, quotients, and powers of expressions with exponents. They simplify calculations involving products and ratios of powers of ten.
International System of Units: The internationally standardized system of measurement units and their definitions. Its decimal prefixes express multiples and fractions of units as powers of ten.
Long and short scales: Two systems for assigning names such as billion to large powers of ten. They demonstrate that spoken number names do not always identify the same power of ten.
Integer: A whole number that may be positive, negative, or zero. The exponent in this concept is restricted to integers.
Negative exponent: An exponent below zero, defined by the reciprocal of the corresponding positive power. It makes powers of ten represent decimal fractions such as one hundredth.
SI prefix: A standardized prefix indicating a decimal multiple or fraction of a measurement unit. Prefixes such as kilo and milli correspond to powers of ten.
Avogadro constant: The number of specified entities in one mole, exactly 6.02214076 × 10²³. Its scientific notation uses a large power of ten to express a counting scale.
Decimal numeral system: A positional numeral system that uses ten as its base and digits from zero to nine. Its place values are successive powers of ten.
Order of magnitude: A scale estimate expressed as a power of ten. Comparing exponents quickly reveals how many decimal scales separate quantities.

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