Celsius and Fahrenheit ConversionsDate: 09/15/97 at 18:09:48 From: Anonymous Subject: Fahrenheit and Celsius Dr. Math: I know that at -40 degrees Celsius and Fahrenheit the metric and English temperatures are the same. I am having problems with the conversion method - I just don't understand. My question is: For what value of C (if any) do both scales represent temperature? C = 5/9 (F-32) or F=9/5( F+32) or how do you set the two different formulas up? Thank you. Kimberly Date: 09/15/97 at 19:16:16 From: Doctor Anthony Subject: Re: Fahrenheit and Celsius Both scales represent temperature, and the formula C ------- = 5/9 F - 32 allows you to convert from one scale to the other. Example. Convert a temperature of 180 degrees F to degrees C. This means that the letter F in the formula is replaced by 180. C -------- = 5/9 C = (5/9) x 148 = 82.22 degrees C 180-32 Example(2). Convert 38 degrees C to degrees F. Now we replace the C in the formula with 38 and find the value of F. 38 5 -------- = ---- F - 32 9 9 x 38 = 5(F-32) 342 = 5F - 160 502 = 5F 100.4 = F so 38 degrees C is the same as 100.4 degrees F. If you have a lot of conversions to make, it is sensible to draw a graph with degrees C along the horizontal axis (say from 0 to 100 degrees) and degrees F up the vertical axis from 32 to 212. If you plot the points (0,32) and (100,212) and join these points with a straight line, then you can read from one scale to the other with the minimum of effort. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 09/16/97 at 09:51:30 From: Anonymous Subject: Re: Fahrenheit and Celsius This is my question.... For what value of C (if any) do both scales represent the temperature? Thank you, Kimberly Date: 09/22/97 at 12:47:22 From: Doctor Rob Subject: Re: Fahrenheit and Celsius I think you are referring to the Fahrenheit and Celsius temperature scales. The relation is F = 9*C/5 + 32, where F is the temperature in degrees Fahrenheit, and C is the temperature in degrees Celsius. To find where the number of degrees is the same on both scales, solve that equation simultaneously with F = C. This gives you two first-degree equations in the two unknowns F and C. Use one equation to solve for one of the variables. Substitute it into the other equation. This will give you one first-degree equation in the other unknown. Solve that for that unknown. Use its value to find the first unknown using the formula you derived in the first step. Hint: Brrrrr! -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/