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How heavy is 0.001 ounces?

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It's about 0.000000008 times as heavy as a Hippopotamus.
In other words, 0.001 ounces is 0.000000007560 times the weight of a Hippopotamus, and the weight of a Hippopotamus is 132,000,000 times that amount.
(Hippopotamus amphibius) (adult, male)
The average weight of an adult male hippopotamus ranges from 132,000 ounces. Appearances to the contrary, adult hippos cannot swim or float in water; they actually move by leaping and walking across lake bottoms at about 8 kph (5 mph).
It's about 0.000000005 times as heavy as an Elephant.
In other words, 0.001 ounces is 0.00000000470 times the weight of an Elephant, and the weight of an Elephant is 210,000,000 times that amount.
(for African bush elephant, Loxodonta africana) (Adult, bull)
A bull African bush elephant weighs about 220,000 ounces. Among African elephants, both males and females have tusks (whereas female Asian elephants, Elephas maximus, do not have tusks) which can grow to 3 m (10 ft) and typically weigh about 140,000 ounces
It's about 0.000000005 times as heavy as a Tyrannosaurus rex.
In other words, 0.001 ounces is 0.00000000440 times the weight of a Tyrannosaurus rex, and the weight of a Tyrannosaurus rex is 230,000,000 times that amount.
(for FMNH PR2081, a.k.a. "Sue") (a.k.a. Tyrannosaurus, a.k.a. T-Rex) (estimated live weight)
The notable Tyrannosaurus specimen housed at the Field Museum of Natural History in Chicago, Illinois, "Sue," is estimated to have weighed about 230,000 ounces while alive. A renowned predator in popular culture, the teeth of tyrannosaurus rex were up to 33.02 cm (13 in) long.
It's about 0.000000003 times as heavy as an Anchor of a Cruise Ship.
In other words, 0.001 ounces is 0.000000002510 times the weight of an Anchor of a Cruise Ship, and the weight of an Anchor of a Cruise Ship is 398,000,000 times that amount.
(for QE2 forward anchor, a.k.a. RMS Queen Elizabeth 2)
Each of the forward anchors of the RMS Queen Elizabeth 2 weighs 399,000 ounces. The anchor of the QE2 now sits in front of the Holyrood Church in Southampton, England, United Kingdom, along a pedestrian tourist route known as "the QE2 mile."
It's about 0.0000000004 times as heavy as The Space Shuttle.
In other words, 0.001 ounces is 0.000000000400 times the weight of The Space Shuttle, and the weight of The Space Shuttle is 2,500,000,000 times that amount.
(for Endeavour, a.k.a. OV-105, a.k.a. Orbiter Vehicle-105) (empty weight, excluding main engines)
When empty, the space shuttle Endeavour weighs 2,500,000 ounces. The shuttle's spacious cargo bay carried the Chandra X-ray Observatory into orbit in 1999 — a payload that weighed 700,000 ounces.
It's about 0.0000000003 times as heavy as a Blue Whale.
In other words, 0.001 ounces is 0.0000000002710 times the weight of a Blue Whale, and the weight of a Blue Whale is 3,690,000,000 times that amount.
(Balaenoptera musculus)
Blue whales weigh between 3,690,000 ounces. The largest mammal to have ever lived, blue whales feed almost exclusively on krill — tiny invertebrates weighing about 0.0353 ounces each.
It's about 0.0000000002 times as heavy as a House.
In other words, 0.001 ounces is 0.0000000001820 times the weight of a House, and the weight of a House is 5,490,000,000 times that amount.
(149 sq. m, single-level, unfurnished)
A 149 sq. m (1,600 sq. ft), single-story, unfurnished house (without extensive masonry) of the type commonly found in America would weigh approximately 5,500,000 ounces, based on the weight of the included materials. In contrast, a yurt — a type of dwelling structure popular among nomadic peoples of East Asia — typically weighs less than 16,200 ounces.