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Distribution of Numbers and Distribution of Significant Figures

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Abstract

IN an earlier note1 it is shown that the distribution of first digits of the numbers in a table will obey a logarithmic law provided that a certain sum can be replaced by an integral. We shall here discuss this approximation in more detail. The notation used will be the same as before, f(x) giving the distribution of the numbers and F(p) the distribution of the significant figures. We shall also introduce the distribution of the logarithms of the numbers; setting y = In x, we have for the fraction of entries with logarithms between y and y + dy:

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References

  1. Nature, 154. 800 (1944).

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Authors and Affiliations

  1. Harvard University, Cambridge, Mass.

    W. H. FURRY

  2. Ithaca, New York

    HENRY HURWITZ

Authors
  1. W. H. FURRY
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  2. HENRY HURWITZ
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FURRY, W., HURWITZ, H. Distribution of Numbers and Distribution of Significant Figures. Nature 155, 52–53 (1945). https://doi.org/10.1038/155052a0

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