2 way equation? (which is right?)

RuroumiKenshin
2 way equation??!! (which is right?)

I'm used to the formula(for converting celcius in to farenhiet):
c=f+ 30 x 2. BUT, in some book (call it book B), its different. You just use F= 9/5 (C-32) and replace C with the given celcius temprature and multiply every thing by 9/5. Anyhow, I used both formulas, and got 2 different answers (and checked my work). Personally, I think the way book B put it doesn't make sense. If it makes sense to you, please explain.

HallsofIvy
Homework Helper
Either you have a whole stack of books that should be thrown out or you are not reading them very closely. Both formulas are wrong!

For one thing you must surely know that 0 degrees Celcius is 32 degrees Fahrenheit so you can use that as a check:
Using your formula: c=f+ 30 x 2 (as you wrote it) f= 32 would give c= 32+ 60= 96! Of course, you really meant c= (f+32)*2 but that would be 64*2= 128 which is even worse! c= (f-32)*2 would give c=0 for f= 32 but gives c= (212-32)*2= 180*2= 360 degrees for the boiling point of water when it should be 100 degrees.

The formula you give for "book B":F= 9/5 (C-32) is almost exactly backwards: it should be C= (5/9)(F-32) (or F= (5/9)C + 32) so that when F= 32, C= 0 and when F= 212, C= (5/9)(180)= 5(20)= 100 degrees.

Originally posted by HallsofIvy
[ The formula you give for "book B":F= 9/5 (C-32) is almost exactly backwards: it should be C= (5/9)(F-32) (or F= (5/9)C + 32) so that when F= 32, C= 0 and when F= 212, C= (5/9)(180)= 5(20)= 100 degrees.

These formulas are incompatible. Surely you mean F = (9/5)C +32???

what i learn also F=(9/5)C + 32 F
when C = -40....F= -40 also...
and use calculator can get the same answer

Let me (try to) make everything clear.
Take two test points :
0 C 32 F
100 C 212 F
X C Y F
(Tell me if my test points are wrong, i am not familiar with the fahrenhite system)
Now, try to solve the problem

Now, we know that the relation between X and Y is linear, so :
Y=aX+b
Apply this to the two test points
32=a*0+b
so ... b=32
Apply this to the second test point
212=a*100+32
(212-32)/100=a
a=1.8
So:
Y=1.8*X+32
or (the way people understand it more)
F = 1.8C + 32

And this is the right equation (isn't it ?)

^Yes.

Integral
Staff Emeritus
Gold Member
I frequently use an approximation which resembles VMs first equation

C= (F-32)/1.8 ~ (F-30)/2

or
F= (1.8C)+32 ~ (2C)+30

The last of those relationships is much easier to do in your head and for normal temps is pretty close.

edit: opps! I fixed a sign error in the last line

Last edited:
RuroumiKenshin
Here's what book A says:
"We frequently want to convert from one scale to another, so we need a convenient formula to help us with the conversion. The formula C= 5/9 (F-32) shows us the relationship between Celsius and Fahrenheit and allows us to change form one scale or another.
Example one:
Change 77 degrees Fahrenheit to Celsius.

Analysis:
Let F= the Fahrenheit temprature
Let C= the Celsius temprature

We'll use our formula and then simply substitute 77 for F.

Work:
C=5/9(F-32) F=77:
C=5/9(77-32)
C=5/9(45)
C=25

"Example 2:
Find the Fahrenheit equivalent of 55 degrees Celsius.

Analysis:"
F= Fahrenheit
C= Celsius
"Use the same formula and then just substitue 55 for Celsius.

Work:
C= 5/9(F-32) C=55:
55=5/9(F-32)

Multiply by 9/5: 9/5(55=5/9(F-32)
99=F-32

And Book B:

"F= 9/5C+ 32" (the book basically tells you to solve for C)."

"You can estimate temprature in degrees Fahrenheit by the formula
F=2 x C+30"

HallsofIvy