Dealing with very large and very small numbers

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SUMMARY

The discussion focuses on the accuracy of various approximations related to large and small numbers, specifically distances and masses. The distance from Earth to the Sun is confirmed as 90 million miles or 144 million kilometers, while the distance to the Moon is accurately stated as 240 thousand miles or 400 thousand kilometers. The mass of the Earth is correctly approximated at 6 x 10^24 kg. However, there is a correction regarding the mass of an electron, where the original claim of 9 x 10^-31 kg is clarified to be equivalent to 90 nonillionths of a kg, with the correct interpretation of nonillionths and octillionths highlighted.

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  • Basic knowledge of astronomical distances, specifically between Earth, the Sun, and the Moon.
  • Familiarity with mass measurements in kilograms and grams.
  • Concepts of numerical approximations and their significance in scientific contexts.
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Students, educators, and professionals in fields such as physics, astronomy, and mathematics who require a clear understanding of large and small number representations and their applications in scientific contexts.

Cliff Hanley
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Are the following correct (all numbers are approximations);

d from the Earth to the Sun is 90 million miles = 9 x 10^ 7 miles = 144 million km = 1.44 x 10 ^ 8 km ?

d from the Earth to the Moon is 240 thousand miles = 2.4 x 10^ 5 miles = 400 thousand km = 4 x 10 ^ 5 km?

m of the Earth = 6 x 10 ^ 24 kg = 6 septillion kg = 6 trillion trillion kg ?

m of electron = 9 x 10 ^ -31 kg = 90 nonillionths of a kg = 9 x 10 ^ -28 g = 90 octillionths of a g ?
 
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I think your last line is wrong.
A nonillionth should be 10^-30. So 10^-31 is 1 tenth of a nonillionth.
Same thing with octillionths, 9x 10^-28 = .9 x 10^-27, or .9 octillionths, which would be 900 nonillionths.
 
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