<p>The fifth root of 100 is occasionally referred to as <a href="https://mathworld.wolfram.com/PogsonsRatio.html" rel="noreferrer">&quot;Pogson's Ratio&quot;</a> after Norman Pogson who systematized the magnitude system.  I'd recommend <em>not</em> using this as it doesn't save any space or time and only serves to disguise a value that actually is a fifth root.</p>
<p>As 100 is not a fifth power, the fifth root of 100 is irrational. All roots of integers are either irrationals or integers.</p>

CC BY-SA 4.0
2024-04-04T09:56:00.623Z
Another reason not to use the term "Pogson's ratio": A survey among nine astronomer colleagues yielded zero astronomers who had ever heard the term before :)
pela
CC BY-SA 4.0
2024-05-09T04:38:48.860Z
Do you have the resource where you found this? I find this very interesting and couldn't find anything online. Thanks for sharing the fun fact :)
Astrovis
CC BY-SA 4.0
2024-05-09T04:41:15.643Z
Yes, linked in the question https://mathworld.wolfram.com/PogsonsRatio.html
James K
CC BY-SA 4.0
2024-04-04T06:33:41.063Z
2024-04-04T06:33:41.063Z
James K
<p>I understand that each scale you go up on the absolute magnitude scale, the luminosity decreases by the fifth root of 100, or around 2.512. Is there a name for the constant 2.512, or not. Also, is the fifth root of 100 rational, or irrational?</p>

CC BY-SA 4.0
2024-04-04T05:00:16.490Z
https://math.stackexchange.com/questions/1012377/can-any-root-such-as-a-square-root-or-a-cube-root-be-rational Thiis suggests the answer to the latter question is "irrational".
Allure
<mathematics><apparent-magnitude><luminosity><magnitude><absolute-magnitude>
Is there a specific constant name for the fifth root of 100?
Astrovis
# Is there a specific constant name for the fifth root of 100?

(Asked by: username_0 on 2024-04-04)

I understand that each scale you go up on the absolute magnitude scale, the luminosity decreases by the fifth root of 100, or around 2.512. Is there a name for the constant 2.512, or not. Also, is the fifth root of 100 rational, or irrational?

**Tags:** mathematics, apparent-magnitude, luminosity, magnitude, absolute-magnitude

> **Comments:**
> **username_1**: https://math.stackexchange.com/questions/1012377/can-any-root-such-as-a-square-root-or-a-cube-root-be-rational Thiis suggests the answer to the latter question is "irrational".  

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## 1 answers

### Answer by username_2 on 2024-04-04. Score: 6 | Accepted answer

The fifth root of 100 is occasionally referred to as ["Pogson's Ratio"](https://mathworld.wolfram.com/PogsonsRatio.html) after Norman Pogson who systematized the magnitude system. I'd recommend *not* using this as it doesn't save any space or time and only serves to disguise a value that actually is a fifth root.

As 100 is not a fifth power, the fifth root of 100 is irrational. All roots of integers are either irrationals or integers.

> **Comments:**
> **username_3**: Another reason not to use the term "Pogson's ratio": A survey among nine astronomer colleagues yielded zero astronomers who had ever heard the term before :)  
> **username_0**: Do you have the resource where you found this? I find this very interesting and couldn't find anything online. Thanks for sharing the fun fact :)  
> **username_2**: Yes, linked in the question https://mathworld.wolfram.com/PogsonsRatio.html  

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