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How long is 3,000 meters?

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It's about one-and-a-half times as long as The Kentucky Derby
In other words, 3,000 meters is 1.491290 times the length of The Kentucky Derby, and the length of The Kentucky Derby is 0.670560 times that amount.
(Churchill Downs, Louisville, Kentucky) (total race length)
The total race length of the Kentucky Derby run at Churchill Downs is 2,011.680 meters. First run in 1864, the Kentucky Derby is one of the oldest continuously-running sporting events in America, almost two years older than the Westminster Kennel Club Dog Show
It's about one-and-three-fifths times as long as The Preakness Stakes
In other words, 3,000 meters is 1.569780 times the length of The Preakness Stakes, and the length of The Preakness Stakes is 0.63703190 times that amount.
(Pimlico Race Course, Baltimore, Maryland) (total race length)
The total race length of the Preakness Stakes run at the Pimlico Race Course is 1,911.096 meters. Dubbed "the race for the Black-eyed Susans" after Maryland's state flower, the winning horse is actually draped with a garland of painted yellow daisies, as Black-eyed Susans do not bloom in time for the late-May race.
It's about three-fifths as tall as a Puncak Jaya
In other words, 3,000 meters is 0.61430 times the height of a Puncak Jaya, and the height of a Puncak Jaya is 1.6280 times that amount.
(a.k.a. Mt. Carstensz, a.k.a. Carstensz Pyramid, a.k.a. Nemangkawi, a.k.a. Carstensz Toppen, a.k.a. Gunung Sukarno) (Papua province, Indonesia)
The highest point in Oceania (and therefore one of the seven summits) peak of Puncak Jaya is 4,884 m. Dutch explorer Jan Carstenszoon, the mountain's namesake, is said to have been ridiculed for claiming to have seen snow near the equator when he reported his discovery of the peak in 1623.
It's about three-fifths as tall as a Vinson Massif
In other words, 3,000 meters is 0.61320 times the height of a Vinson Massif, and the height of a Vinson Massif is 1.6310 times that amount.
(a.k.a. Mount Vinson) (Antarctica)
Mount Vinson, the highest peak of the Vinson Massif mountain, reaches 4,892 m at its peak. The mountain is named after Georgia Congressman Carl Vinson who emphatically promoted Antarctic exploration in the 1930s.
It's about half as tall as Mount Elbrus
In other words, 3,000 meters is 0.53170 times the height of Mount Elbrus, and the height of Mount Elbrus is 1.8810 times that amount.
(a.k.a. Mingi Tau, a.k.a. Эльбрус, a.k.a. იალბუზი) (Karachay-Cherkessia and Kabardino-Balkaria, Russia) (west summit)
The west summit of the dual-summit volcano Mount Elbrus is 5,642 m at its peak and is the highest peak in both Russia and the European continent. Until 1976, a cable car would take visitors to the mountain as far up as the Garabashi camp, located at an elevation of 3,800 m.
It's about half as tall as a Kilimanjaro
In other words, 3,000 meters is 0.509270 times the height of a Kilimanjaro, and the height of a Kilimanjaro is 1.963590 times that amount.
(a.k.a. Mount Kilimanjaro) (Tanzania) (to Uhuru peak; 2008 gravimeter measurement)
Kilimanjaro rises to 5,890.79 m at its peak. An isolated peak with no surrounding mountain range, Kilimanjaro is considered the world's tallest freestanding mountain.
It's about half as tall as Mount Logan
In other words, 3,000 meters is 0.50340 times the height of Mount Logan, and the height of Mount Logan is 1.9860 times that amount.
(Kluane National Park and Reserve, Yukon, Canada) (elevation)
The highest mountain in Canada, Mount Logan has a total height of 5,960 m. The high altitude and northern latitude of the mountain resulted in one-time temperature of -77.5 °C — the lowest temperature ever recorded outside of Antarctica.