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?

How do you come up with a formula where the absolute value of K=F?

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2014.05.0130 Jul '12 14:241 edit

Take the usual formula for K to F:*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?(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- Joined
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slatington, pa, usa30 Jul '12 15:41

I am talking about the absolute value of K Vs absolute value of F, not C.*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:

[/b]**(c-273.15)*1.8+32=c**=c

Solve for c:

1.8c-491.67+32=c

-459.67=-0.8c

[b]574.5875

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.- Joined
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2014.05.0130 Jul '12 17:044 edits

Ahh, now I know what you want. I didn't understand exactly what you were asking for in the opening post.*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.

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

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. ðŸ™‚- Joined
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slatington, pa, usa30 Jul '12 17:351 edit

I used the windows PC calculator and got this:*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. ðŸ™‚

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. ðŸ™‚

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.- Joined
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2014.05.0130 Jul '12 22:011 edit

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 ðŸ˜›].*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.

45967/280 does the trick in this case.- Joined
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slatington, pa, usa31 Jul '12 01:162 edits

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.*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 ðŸ˜›].**

45967/280 does the trick in this case.

How did you suss out that fraction anyway? You have fraction sniffing software?- Joined
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2014.05.0131 Jul '12 01:461 edit

My windows calc program gives*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?

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. ðŸ™‚

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.

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slatington, pa, usa31 Jul '12 11:04

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.*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. ðŸ™‚

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.

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2014.05.0131 Jul '12 13:462 edits

I*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.***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).- Joined
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slatington, pa, usa31 Jul '12 13:56

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?*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).- Joined
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2014.05.0131 Jul '12 14:15

You always include all repeating digits. You just write down enough to make sure they are lined up for the subtraction.*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?**- Joined
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