I'm not sure if this is the right place for this question, but here goes...

I'm reviewing literature regarding effectiveness of wastewater treatment techniques. When considering faecal coliforms concentrations are generally presented in terms of most probable number per volume or per mass, typically MPN/100mL or MPN/g. Due to the scales involved these are often in scientific notation. The reduction in concentration due to treatment is then presented as a log factor, i.e. reduction from $6\times10^{10}MPN/100mL$ to $3\times10^{4}MPN/100mL$ is hence $log(2\times10^{6}) = 6.30$.

One paper that I'm reading presents the following (amongst several similar examples):

influent Faecal coliform conc. = 


effluent Faecal coliform conc. = 


resultant log reduction = 2.18

1: Has anyone encountered data presented like this before?

2: Is there some way of calculating reduction that results in 2.18 (I get 2.05)?

I contacted the author re. the data presentation, to be told: "While showing your results you can follow any kind of mode to compare your results. It is up to you that how you are interpretating your data. But, whenever you showing these data it should not be in decimal place it would be in 10 to the power. And that superscript can be in decimal."


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    $\begingroup$ I must be missing something because a number like 1.43e5.1 doesn't make any sense to me. I assume it means $1.43\times10^{5.1}$ but that is really weird notation. $\endgroup$ – MaxW Oct 1 '17 at 23:01
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    $\begingroup$ My understanding of the notation is the same, but I find the values of the exponents weird. I would have expected integer values, ie 5 not 5.1. My handheld calculator doesn't handle exponents with decimals, just integer values. $\endgroup$ – Fred Oct 1 '17 at 23:20
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    $\begingroup$ The author also commented: "Whatever data has been represented in this paper all are very explicit manner. I followed the given method just because of comparing my results from the initial influent concentration." I tried to get further explanation, highlighting how using different fractional exponents for mean and s.d. made for difficult interpretation, but the email dialogue dried up. So, before approaching the publisher of the journal, I thought I'd ask around (here) in case it was me being a numpty.... $\endgroup$ – jack_sprat Oct 1 '17 at 23:47
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    $\begingroup$ I'd write $1.43\times10^{5.1}$ as 1.80e5 meaning $1.80\times10^5$. I can't see any reason to use weird notation. I've read thousands of papers on analytical chemistry and never ran across fractional exponents. $\endgroup$ – MaxW Oct 1 '17 at 23:55
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    $\begingroup$ Furthermore, 1.43e5.1 +/- 0.6e0.35 equates to : 1.8e5 +/- 1.34, which is a suspiciously tiny s.d. relative to the mean - somebody must be VERY good at counting bacteria! $\endgroup$ – jack_sprat Oct 2 '17 at 1:29

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