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

<p>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 $log(2\times10^{6}) = 6.30$.</p>

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

<pre><code>influent Faecal coliform conc. = 
</code></pre>

<p>$1.43\times10^{5.1}\pm0.6\times10^{0.25}MPN/100mL$ <br></p>

<pre><code>effluent Faecal coliform conc. = 
</code></pre>

<p>$5.1\times10^{2.5}\pm3.7\times10^{0.7}MPN/100mL$ <br></p>

<pre><code>resultant log reduction = 2.18
</code></pre>

<p>1: Has anyone encountered data presented like this before?</p>

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

<p>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."</p>

<p>JS</p>

CC BY-SA 3.0
2017-10-01T23:01:44.960Z
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.
MaxW
CC BY-SA 3.0
2017-10-01T23:16:56.570Z
@MaxW: correct, I was using 1.43e5.1 as shorthand for 1.43 x10^5.1, but I don't know how to achieve your formatting on here... you may have seen the 0.00e00 notation form on e.g. MS-Excel
jack_sprat
CC BY-SA 3.0
2017-10-01T23:20:09.780Z
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.
Fred
CC BY-SA 3.0
2017-10-01T23:23:04.710Z
Jack - Any explanation of why you would need a fractional exponent?!? That is just really really weird.
MaxW
CC BY-SA 3.0
2017-10-01T23:47:39.177Z
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....
jack_sprat
CC BY-SA 3.0
2017-10-01T23:55:55.803Z
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.
MaxW
CC BY-SA 3.0
2017-10-02T00:29:52.387Z
@jack_sprat: like you, I got a log reduction of 2.05 (2.048)
Fred
CC BY-SA 3.0
2017-10-02T01:29:42.447Z
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!
jack_sprat
<pollution>
Present results as log data
jack_sprat
# Present results as log data

(Asked by: username_0 on 2017-10-01)

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. = 

```

$1.43\times10^{5.1}\pm0.6\times10^{0.25}MPN/100mL$

```
effluent Faecal coliform conc. = 

```

$5.1\times10^{2.5}\pm3.7\times10^{0.7}MPN/100mL$

```
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."

JS

**Tags:** pollution

> **Comments:**
> **username_1**: 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.  
> **username_0**: @username_1: correct, I was using 1.43e5.1 as shorthand for 1.43 x10^5.1, but I don't know how to achieve your formatting on here... you may have seen the 0.00e00 notation form on e.g. MS-Excel  
> **username_2**: 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.  
> **username_1**: Jack - Any explanation of why you would need a fractional exponent?!? That is just really really weird.  
> **username_0**: 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....  
> **username_1**: 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.  
> **username_2**: @username_0: like you, I got a log reduction of 2.05 (2.048)  
> **username_0**: 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!  

---

## 0 answers

