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Reducing Scales - Recurring numbers & Patterns

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Renegade:
Here's a fun one:

1/81

:D

vlastimil:
It is called repeating decimal or recurring decimal, so you were very very close. The infinity sign is not used - instead there should be a horizontal line above the digits that are repeating ( not easily done in html ;-) ).

Rational numbers (M/N, where M and N are integral) do have this property when they are written in the usual decimal notation. Look these examples:
1.2 = 12/10
1.23 = 123/100
1.234 = 1234/1000
These "normal" decimal numbers can be expressed as fractions, but note that there always is a power of 10 in denominator. Our usual decimal notation can be considered just a shortcut of the full M/N notation.

Every fractional number (that cannot be further simplified) that has something else than a product of 2s and 5s (10=2*5) in the denominator will have infinite number of repeating digits when written in decimal notation.
1/3, 1/6, 1/7, 1/9, 1/11, 1/13, ...

Here is a provocative number: 1/2 = 0.5 = 0.500000000000000000000000000000000000...  :D

Renegade:
It is called repeating decimal or recurring decimal, so you were very very close. The infinity sign is not used - instead there should be a horizontal line above the digits that are repeating ( not easily done in html ;-) ).
-vlastimil (December 04, 2012, 11:00 AM)
--- End quote ---

But CSS works! :D


--- Code: CSS ---.bar {border-top: 1px solid #000000;}

tomos:
Thanks for the explanations Vlastimil
it's interesting - I've never really thought about these basics before...

tomos:
Every fractional number (that cannot be further simplified) that has something else than a product of 2s and 5s (10=2*5) in the denominator will have infinite number of repeating digits when written in decimal notation.
1/3, 1/6, 1/7, 1/9, 1/11, 1/13, ...
-vlastimil (December 04, 2012, 11:00 AM)
--- End quote ---

so, I think the reason I got the same recurring decimal twice, was simply because, in both cases, the number was divided by 7.
(Also the numbers being divided are related.)

the first instance was:
1000/7
and in the second example it would have needed
500/7 to get the correct percentage.

So naturally the second result is half the first 1000 -> 500

Very simple really - once I get a break from it - and get a maths lesson :Thmbsup:

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