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The ratio of the distance of the sun from the earth to that of the moon from the earth is of the order of

  • A.\(10^{7}\)
  • B.\(10^{3}\)
  • C.\(10^{6}\)
  • D.\(10^{8}\)
  • E.\(10^{-4}\)

Answer: B

The ratio is of the order of \(10^{3}\).

The Sun is about \(1.5 \times 10^{11}\) m from the Earth and the Moon about \(3.84 \times 10^{8}\) m:

\[ \frac{1.5 \times 10^{11}}{3.84 \times 10^{8}} \approx 390 \]

Since \(\log_{10}390 \approx 2.6\), the nearest power of ten is \(10^{3}\). The larger powers would put the Sun millions of times farther than the Moon, and \(10^{-4}\) inverts the ratio.

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