1. Subscribersonhouse
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    30 Jul '12 10:34
    I got close just doing the formula, (((K-273.15)*1.8)-32)=F
    How do you come up with a formula where the absolute value of K=F?
  2. Standard memberSwissGambit
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    30 Jul '12 14:241 edit
    Originally posted by sonhouse
    I got close just doing the formula, (((K-273.15)*1.8)-32)=F
    How do you come up with a formula where the absolute value of K=F?
    Take the usual formula for K to F:
    (K-273.15)*1.8+32=F
    We want to find the point at which the temp value is the same for both scales, so substitute:
    (c-273.15)*1.8+32=c
    Solve for c:
    1.8c-491.67+32=c
    -459.67=-0.8c
    574.5875=c
  3. Subscribersonhouse
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    30 Jul '12 15:41
    Originally posted by SwissGambit
    Take the usual formula for K to F:
    (K-273.15)*1.8+32=F
    We want to find the point at which the temp value is the same for both scales, so substitute:
    (c-273.15)*1.8+32=c
    Solve for c:
    1.8c-491.67+32=c
    -459.67=-0.8c
    [b]574.5875
    =c
    [/b]
    I am talking about the absolute value of K Vs absolute value of F, not C.

    It is ~164, that is 164 degrees K = ~-164 degrees F, just wanted to see if there was an exact solution and how you derive a formula that would give that exact solution.
  4. Standard memberSwissGambit
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    30 Jul '12 17:044 edits
    Originally posted by sonhouse
    I am talking about the absolute value of K Vs absolute value of F, not C.

    It is ~164, that is 164 degrees K = ~-164 degrees F, just wanted to see if there was an exact solution and how you derive a formula that would give that exact solution.
    Ahh, now I know what you want. I didn't understand exactly what you were asking for in the opening post.

    The variable "c" was not meant to be Celsius, but a generic variable. Sorry about the confusion. I will use "x" this time. 🙂

    The steps are the same as before. Just start with -x on the right side this time:
    (x-273.15)*1.8+32=-x
    1.8x -491.67+32=-x
    -459.67=-2.8x
    x=164.1678571


    Edit: But if you speak in terms of absolute value, then both of my answers are solutions. 🙂
  5. Subscribersonhouse
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    30 Jul '12 17:351 edit
    Originally posted by SwissGambit
    Ahh, now I know what you want. I didn't understand exactly what you were asking for in the opening post.

    The variable "c" was not meant to be Celsius, but a generic variable. Sorry about the confusion. I will use "x" this time. 🙂

    The steps are the same as before. Just start with -x on the right side this time:[quote](x-273.15)*1.8+32=-x
    1.8x ...[text shortened]... t if you speak in terms of absolute value, then both of my answers are solutions. 🙂
    I used the windows PC calculator and got this:


    164.1678571 428571 428571 428571.....

    I separated the digits by the 1's to show the repeating series.

    I wonder if there is a way, perhaps another number base, that would make that an exact solution, somewhat akin to the difference between calling it 4.333333333....Vs
    4 1/3 (exact solution)

    So in base 10, there is no exact solution just an infinite series.
  6. Standard memberSwissGambit
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    30 Jul '12 22:011 edit
    Originally posted by sonhouse
    I used the windows PC calculator and got this:


    164.1678571 428571 428571 428571.....

    I separated the digits by the 1's to show the repeating series.

    I wonder if there is a way, perhaps another number base, that would make that an exact solution, somewhat akin to the difference between calling it 4.333333333....Vs
    4 1/3 (exact solution)

    So in base 10, there is no exact solution just an infinite series.
    If there is a repeating decimal, it can be expressed as a fraction. You don't need another number base [not sure why that would help anyway 😛].

    45967/280 does the trick in this case.
  7. Subscribersonhouse
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    31 Jul '12 01:162 edits
    Originally posted by SwissGambit
    If there is a repeating decimal, it can be expressed as a fraction. You don't need another number base [not sure why that would help anyway 😛].

    45967/280 does the trick in this case.
    Well my calculator says 45967/280 covers the 164.1678571 part exactly but it misses out on the actual repeaters, the 428571's that repeat forever.

    How did you suss out that fraction anyway? You have fraction sniffing software?
  8. Standard memberSwissGambit
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    31 Jul '12 01:461 edit
    Originally posted by sonhouse
    Well my calculator says 45967/280 covers the 164.1678571 part exactly but it misses out on the actual repeaters, the 428571's that repeat forever.

    How did you suss out that fraction anyway? You have fraction sniffing software?
    My windows calc program gives

    164.1678571 428571 428571 428571 4286

    I am not sure why you are not seeing the repeating digits. You should.

    I used an old algebra trick to get the fraction. Software didn't come into play until it was time to reduce the fraction. 🙂

    N = 164.1678571 428571 428571

    create another equation by multiplying both sides by some power of 10, such that the repeating digits line up with the first equation:

    1000000N = 164167857.1428571 428571

    Now subtract the first equation from the second:

    999999N = 164167692.975

    get rid of the decimals:

    999999000N = 164167692975

    solve for N and you have your fraction:

    164167692975/999999000

    now all that remains is to reduce it.

    45967/280
  9. Subscribersonhouse
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    31 Jul '12 11:04
    Originally posted by SwissGambit
    My windows calc program gives

    164.1678571 428571 428571 428571 4286

    I am not sure why you are not seeing the repeating digits. You should.

    I used an old algebra trick to get the fraction. Software didn't come into play until it was time to reduce the fraction. 🙂

    N = 164.1678571 428571 428571

    create another equation by multiplying both sid ...[text shortened]... your fraction:

    164167692975/999999000

    now all that remains is to reduce it.

    45967/280
    but with that method don't you need to include all the infinite number of repeats? That would seem to me to need an infinite number of zeros in the first part, 1000000000000000000000000000..........N to get the whole thing.
  10. Standard memberSwissGambit
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    31 Jul '12 13:462 edits
    Originally posted by sonhouse
    but with that method don't you need to include all the infinite number of repeats? That would seem to me to need an infinite number of zeros in the first part, 1000000000000000000000000000..........N to get the whole thing.
    I did include the infinite repeats. They were there when I subtracted one equation from the other, but they were lined up, and thus disappeared due to the subtraction. It's a pretty sweet trick.

    Here's a simpler example to illustrate.

    Make up some number with repeating digits:

    14.512 757575757575...

    Created 2nd equation and subtract the first:

    100N = 1451.2 757575757575....
    -(N = 14.512 757575757575....)
    -------------------------
    99N = 1436.763 (the repeating 75's died in the subtraction!)
    99000N=1436763
    N=1436763/99000
    N=478921/33000 (unlucky - this couldn't be reduced much, but there it is. Plug it into a calculator and you should get all the repeating digits).
  11. Subscribersonhouse
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    31 Jul '12 13:56
    Originally posted by SwissGambit
    I did include the infinite repeats. They were there when I subtracted one equation from the other, but they were lined up, and thus disappeared due to the subtraction. It's a pretty sweet trick.

    Here's a simpler example to illustrate.

    Make up some number with repeating digits:

    14.512 757575757575...

    Created 2nd equation and subtract th ...[text shortened]... ch, but there it is. Plug it into a calculator and you should get all the repeating digits).
    So the answer would be the same no matter how many repeating digits were included? It would also be the same if you only used the first set of digits and ignored the rest?
  12. Standard memberSwissGambit
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    31 Jul '12 14:15
    Originally posted by sonhouse
    So the answer would be the same no matter how many repeating digits were included? It would also be the same if you only used the first set of digits and ignored the rest?
    You always include all repeating digits. You just write down enough to make sure they are lined up for the subtraction.
  13. Subscribersonhouse
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    31 Jul '12 16:37
    Originally posted by SwissGambit
    You always include all repeating digits. You just write down enough to make sure they are lined up for the subtraction.
    I'm still stuck on the part where you can't write down an infinite series...
  14. Standard memberSwissGambit
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    01 Aug '12 00:14
    Originally posted by sonhouse
    I'm still stuck on the part where you can't write down an infinite series...
    But why would you need to?
  15. Subscribersonhouse
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    01 Aug '12 01:15
    Originally posted by SwissGambit
    But why would you need to?
    I thought I said that then I thought you said you included the infinite series which is why I'm confused.
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