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

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In summary, there is a more elegant way to express 14% (Base_10) in octal, which would be 0.107 (Base_8). However, if accuracy is required, it can be expressed as 0.112 (Base_8). There are also convenient words for equivalents in Base_8, such as "Nine Gadols" for 14% (Base_10). This is due to the complexity of legacy systems and the use of different base notations.
  • #1
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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  • #2
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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  • #3
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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  • #4
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...
 

1. What is the purpose of expressing a percentage in octal?

The purpose of expressing a percentage in octal is to convert a decimal value to its equivalent in base 8. This can be useful in certain mathematical calculations or for representing data in a different numerical system.

2. How do you convert a percentage from base 10 to octal?

To convert a percentage from base 10 to octal, you can first convert the percentage to a decimal value by dividing it by 100. Then, you can use the remainder method to convert the decimal value to its equivalent in base 8.

3. Can you provide an example of expressing a percentage in octal?

Sure, for example, if we want to express 14% in octal, we can first convert it to a decimal value (0.14) and then use the remainder method to get the octal equivalent, which would be 0.224 (since 0.14 = 0.224 in base 8).

4. Are there any advantages to expressing a percentage in octal?

There may be some advantages in certain situations, such as when working with binary or hexadecimal numbers, as octal is a base 8 system and can be easily converted to and from these bases. However, for general use, it is more common and practical to express percentages in decimal form.

5. Is there a limit to the number of digits in an octal percentage?

Yes, since octal is a base 8 system, the maximum number of digits in an octal percentage would be 8 (0-7). Any additional digits would need to be converted to the next place value, similar to how we convert decimal numbers with more than 10 digits to scientific notation.

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