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PRACTICE / Orders of magnitude

Estimate first, then choose a power of ten

A droplet has volume 2 mm³ and density 1000 kg/m³. The mass of one molecule is approximately 3×10⁻²⁶ kg.

What is the nearest power of ten to its estimated molecule count, using distance on a logarithmic scale?

Organize the givens & assumptions
  • Volume = 2 mm³
  • Density = 1000 kg/m³
  • Molecular mass ≈ 3×10⁻²⁶ kg

Treat the droplet as made of identical molecules with the stated mass. Round the order by nearest log10, so the dividing multiplier is √10.

  1. A101710^{17}
  2. B102010^{20}
  3. C101910^{19}
  4. D102310^{23}

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