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How heavy is 0.001 ounces?

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It's about 0.00000006 times as heavy as a Polar Bear.
In other words, 0.001 ounces is 0.00000005490 times the weight of a Polar Bear, and the weight of a Polar Bear is 18,200,000 times that amount.
(Ursus maritimus) (adult, male)
An adult, male polar bear weighs between 18,200 ounces. Polar bears are so heavily insulated by their 9.9 cm (3.9 in) layer of blubber that they are often difficult to detect using infrared photography sensors.
It's about 0.00000006 times as heavy as a Grizzly Bear.
In other words, 0.001 ounces is 0.00000005440 times the weight of a Grizzly Bear, and the weight of a Grizzly Bear is 18,400,000 times that amount.
(a.k.a. brown bear, a.k.a. silver bear, Ursus arctos horribilis) (Adult, male, coastal area population average)
An adult, male grizzly bear from a coastal area (where food is plentiful) can weigh up to 18,400 ounces. In spite of their tremendous size, grizzly bears can run at speeds of up to 55 kph (34 mph).
It's about 0.00000004 times as heavy as a Cow.
In other words, 0.001 ounces is 0.0000000420 times the weight of a Cow, and the weight of a Cow is 24,000,000 times that amount.
(for Holstein, a.k.a. Holstein Friesian, a.k.a. Friesian, Bos primigenius) (adult, heifer)
A mature Holstein cow (the well-known black-and-white, spotted breed of cow) typically weighs 24,000 ounces. President William Howard Taft (1909 - 1913) kept a Holstein cow named Pauline Wayne on the White House grounds — a gift from a Wisconsin senator and the source of the First Family's milk.
It's about 0.00000002 times as heavy as a Car.
In other words, 0.001 ounces is 0.000000017160 times the weight of a Car, and the weight of a Car is 58,280,000 times that amount.
(for 2009 Ford Taurus; automatic transmission; curb weight)
A 2009 Ford Taurus weighs 58,270 ounces. The first mass-produced car, the Curved Dash Oldsmobile — introduced in 1901 — weighed just 13,620 ounces.
It's about 0.00000002 times as heavy as a Giraffe.
In other words, 0.001 ounces is 0.00000001470 times the weight of a Giraffe, and the weight of a Giraffe is 68,000,000 times that amount.
(Giraffa camelopardalis reticulata) (adult, male, maximum of range)
An adult, male giraffe can weigh up to 68,100 ounces. Reaching 5.5 m (18 ft) in height by adulthood, giraffe calves can grow as much as 3 cm (1 in) per day.
It's about 0.00000002 times as heavy as a Rhinoceros.
In other words, 0.001 ounces is 0.0000000130 times the weight of a Rhinoceros, and the weight of a Rhinoceros is 77,000,000 times that amount.
(for Black rhinoceros, Diceros bicornis) (Adult, male)
An adult black rhinoceros weighs between 74,000 ounces. Rhinoceros are extremely aggressive — nearly one of every two males will die as a result of fighting with other rhinoceros.
It's about 0.000000010 times as heavy as The Tongue of a Blue Whale.
In other words, 0.001 ounces is 0.00000001000 times the weight of The Tongue of a Blue Whale, and the weight of The Tongue of a Blue Whale is 100,000,000 times that amount.
(Balaenoptera musculus) (adult)
The tongue of a Blue Whale can weigh up to 95,000 ounces. Despite their tremendous size, blue whales feed almost exclusively on tiny crustaceans called krill and cannot swallow anything much larger than a beach ball.