How many significant decimal digits for real single precision?

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16

Still confused. For binary32 you have maximum 24 bits to represent a real fraction in memory, which is equivalent to 24 * log10(2) ≈ 7.225 decimal digits or 7 significant digits. So here comes the questions:

  1. Why does fortran intrinsic precision function give 23 * log10(2)≈ 6.924 or 6 significant digits?
  2. where does the “8” or the “9” significant digit come from?