Is there a more elegant way to express eg 14% (Base_10) in Octal?

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Discussion Overview

The discussion revolves around expressing the decimal percentage of 14% in octal notation. Participants explore various methods and representations, including fractional forms and potential equivalents in octal, as well as tangentially mentioning the existence of base-8 slide rules.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire if there is a more elegant way to express 14% (Base_10) in octal than as 11/100 (Base_8).
  • One participant suggests that an octal-based entity might approximate 14% as "about 1/12th" in octal, noting that this is equivalent to 1/10th in decimal.
  • Another participant provides a conversion of 14 (Base_10) to octal fractions, stating that 14/100 (Base_10) can be expressed as 16/144 (Base_8) or 7/62 (Base_8), but expresses confusion over the division process in octal.
  • A participant reflects on the challenges of learning base notation and shares their experience with octal division, arriving at an approximation of 0.107 (Base_8).
  • One participant introduces a creative expression of 14% (Base_10) as "Nine Gadols" in Base_8, though they acknowledge difficulty in finding a better representation for 64 (Base_10) in octal.

Areas of Agreement / Disagreement

Participants express various methods and interpretations without reaching a consensus on a single elegant representation for 14% in octal. The discussion includes differing opinions on approximations and representations, indicating multiple competing views.

Contextual Notes

Some participants express uncertainty about their calculations and conversions, highlighting potential limitations in their understanding of base notation and the division process in octal.

Nik_2213
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Is there a more elegant way to express eg 14% (Base_10) in Octal than as eg 11/100 {Base_8} ?

Tangential: Has any-one seen a Base_8 slide-rule, be-it linear or circular ??
 
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Nik_2213 said:
Is there a more elegant way to express eg 14% (Base_10) in Octal than as eg 11/100 {Base_8} ?

Tangential: Has any-one seen a Base_8 slide-rule, be-it linear or circular ??
Surely, like us, an octal-based critter would round it to the nearest easy fraction - which for them would be "about 1/12th". (Because (Base_8) 1/12th is (Base_10) 1/10th).

But if it had to go for accuracy, they'd dispense with the fractions (as do we) and say "exactly 0.112".

(Did I get those numbers right? I really struggled in base notation in grade school.)
 
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DaveC426913 said:
(Did I get those numbers right? I really struggled in base notation in grade school.)
Well, $$\frac{14_{10}}{100_{10}} = \frac{16_8}{144_8} = \frac{7_8}{62_8}$$ which I'm positive about.

Then I watched a YT vid on dividing in octal and got confused. So, try it the hard way...

<octal>
7/62 = 0%7
70/62=1%6
60/62=0%60
600/62=probably 6 or 7, no clue of the carry.
</octal>

so, I get as far as ##0.107_8## before my failure to memorize the ##10_8 \times## table kicks in. Ah, the follies of youth...
 
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Tangential: Bane of DIY in UK is the zoo of legacy systems. BSP garden taps, any-one ? I grew up with 'Imperial' mensuration, segued to 'scientific. Then I ran into US imports such as HPLC systems that took eg #10-24 and #10-32 UNC/UNF, the latter finger-tight to 200 Bar !!

Extending the above posters' suggestions, I reckoned that, like eg 11_Base10 and 100_Base10 there'd be convenient words for their equivalents_Base8.

I came up with 14% _Base10 == Nine Gadols_Base8 ( To 2½ DP ?) [[ Insert local glyphs for 64Gadolinium ]]

I'm sorry, given Sumerians etc used Base60, my Google-fu failed me on any better way to express 64_Base10...
 

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