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The answer to this question depends on the definition of asteroid. If only objects within the asteroid belt between the orbit of Mars and Jupiter count, then the largest are Ceres, which is about 580 miles (930 km) across and considered a dwarf planet; Vesta, which has a diameter of around 326 miles (525 km); and Pallas, which is about 338 miles (544 km) across, but has less mass than Vesta. These comprise 32%, 9%, and 7% of the asteroid belt's total mass, respectively. If the definition is expanded to include all sub-planet, non-satellite objects in the solar system, including bodies beyond the orbit of Neptune, then the largest are Eris, another dwarf plant with a diameter around 1,445 miles (2,326 km); Pluto, which is about 1,433 miles (2,306 km) across; and Ceres, in that order. By comparison, the Earth has an average diameter of 7,917.5 miles (12,742 km).
To get an idea of the size of the largest asteroids, a person can consider the largest one known to have hit the Earth: it was only about 6 miles (10 km) in diameter. This impact, thought to have occurred about 2 billion years ago, is represented by the Vredefort Crater in South Africa. A similar impact represented by the Sudbury Structure in Canada is dated to 1.8 billion years ago. At the time, only microbes existed as life. The Wilkes Land crater under the East Antarctic ice sheet may signify an even larger impact.
There is one consensus among scientists: the impact of an object larger than 12 miles (20 km) in diameter would be likely to kill all complex life on Earth by blocking out the Sun, halting photosynthesis for years at a time, and causing runaway global cooling. Tens of thousands of cubic kilometers of crust would be instantaneously vaporized, spewing red-hot ejecta across a continent-sized area. The only survivors would be microbes, especially bacteria (extremophiles) and fungi.
Even the third-largest of the asteroids is more than 20 times larger than what is necessary to kill all multicellular life on Earth, if it made impact. Luckily, these objects are in stable orbits and extremely unlikely to cross paths with the planet.
Of the largest, only one has so far been visited by astronauts or space probes. The Dawn mission (launched in 2007) entered orbit around Vesta in July 2011 and left in September 2012, headed to Ceres. New Horizons (launched in 2006) will reach Pluto in 2015. Currently, the best telescopes only provide fuzzy pictures of these bodies, so scientists' knowledge about them is limited. Pluto is known to have a reddish tint, similar to Mars, while Ceres possesses mysterious white and dark spots (presumably craters) that appear and disappear over the years.
In the early history of the solar system, much larger asteroids were common. It is thought that the Moon was created when a Mars-sized object named Rhea formed in the same orbit as the Earth, eventually hitting it. The crust ejected from this impact formed the the Moon. This theory is well-supported because the composition of the Moon is similar to that of the Earth's crust.