Overview
10,000 is the integer that follows 9,999 and precedes 10,001. It is a common round number in everyday counting and planning, often used to express an order of magnitude—ten thousand units. In many languages and cultures the value has a specific name and significance.
Mathematical properties
In the decimal system 10,000 equals 10^4. Its prime factorization is 2^4 × 5^4, so it is both a perfect square (100^2) and a perfect fourth power (10^4). Because the exponents in its factorization are 4 and 4, the number of positive divisors is (4+1)(4+1)=25. The square root of 10,000 is 100, and its digit sum in base ten is 1.
History and names
The Ancient Greek word myriad originally meant 10,000 and later came to mean an indefinitely large number in English. In East Asian number systems a grouping at 10,000 is standard: Chinese wan (萬/万) and Japanese man (万) denote 10,000 and are used as counting units in speech, writing and numeral grouping.
Uses and examples
- Sport: the 10,000-meter track race (10 km) is a standard long-distance athletics event at major competitions.
- Measurement: 10,000 grams equals 10 kilograms; 10,000 meters equals 10 kilometers.
- Health and fitness: 10,000 steps per day is a widely cited daily activity target popularized with consumer pedometers.
- Popular culture: the idea of "10,000 hours" to achieve mastery was popularized in modern writing and debate about skill acquisition.
Notable references and distinctions
Historically, "The Ten Thousand" refers to the army of Greek mercenaries described in Xenophon’s Anabasis, an oft-cited episode in classical history. Numerically, 10,000 serves as one of the common large-round benchmarks in finance, demography and statistics, where it is frequently used to communicate scale without implying precise counts.