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Approximately 3,000,000,000,000, or 3 trillion.

To answer precisely it depends on what the dust is composed of and how much the speck of dust really weighs. I assumed that the average molecular mass of dust was 150 grams/mole (about the weight of 10-12 carbon hydrocarbon), and that a speck of dust weighs 1 microgram (a millionth of a gram or 1 x 10-6 grams).

1 x 10-6 grams ÷ 150 grams/mole = 7 x 10-9 moles

7 x 10-9 moles * 6.02 x 1023 atoms/mole = 4 x 1015 or 4,000,000,000,000,000 or 4 quadrillion

This is approximate as I really don't know the weight of a speck of dust nor its molecular mass, but I think my estimate is reasonable, and if nothing else, I am underestimating the weight of a speck of dust.

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Q: What is the mass of a dust speck?
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