[msandra]

I got a question "Express a temperature of 181K in F"

My calculation is as follow:

Tc + 273 = 181
Tc = -92

Tf = 1.8 (-92) + 32
Tf = -165.6 +32
Tf = -170 + 32 ( 165.6 rounded to 170 becuase -92 is the limiting factor and has 2 sig.fig)

Tf = -138 (to 3 sig. fig)

My prof said I am wrong , and the answer should be -134. Can anyone tell me why?

[jdurg]

Okay.  First you need to remember that T_C = T_k -273.15.  Now, you need to know how to convert Celcius into Fahrenheit.  This is done with the following equation:

T_F =  (T_C)(9/5) + 32.

Now you can convert your Kelvin temperature into Celcius, then convert the Celcius into Fahrenheit.

T_C = 181-273.15 = -92.15.  (Since you are not done with your calculations, you can keep all digits).

T_F = (-92.15)(9/5) + 32 = -133.87.  Now at this point you limit the result by the number of significant figures.  All the digits in the Celcius to Fahrenheit equation do not count since they are exact out to infinity.  Therefore, you're limited by the initial temperature given and the -273.15 used to convert to Celcius.  Therefore, you're limited to 3 significant figures.  This means you would round your result of -133.87 to -134.  That is the correct answer.

[msandra]

If I was given the defination that  K = Tc +273,  

base on your words, even though it gives -92C (2 sig. fig) after summation, does it mean the final should be 3 sig. fig becuase 181K is 3 sig. fig?

I rounded -165.6 to -170 becuase -92 has only 2 sig. fig. does it correct in thinking?

[jdurg]

If you were given the definition that K = Tc + 273, then you would use three significant figures and you would get 92.0 since you are able to use three significant figures.  

Since -92 should have been -92.0, you can use three sig figs and round -165.6 to -166.  When you add 32 to that, you'll get -134.  

[msandra]

Thanks for reply. Just to make sure i get the point :

181K has 3 sig. fig.

by applying the defination K=Tc+273 (273 has unlimited digit because it is defination)

therefore the result gives -92.0 (to 3 sig. fig)

Am I correct?

In another situation, Why does 1101 cm - 1091 cm = 10 cm with 2 significant figures but not 10.00?

Did I mix up with the concept? Please clearify. Thanks

[jdurg]

This will take me some time to get back to you on this.  I had completely forgotten one major rule in regards to sig-figs, so what I wrote out earlier is most likely incorrect.  I'll get back to you on this.