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# Converting Fahrenheit to Celsius

Converting Fahrenheit to Celsius. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

A thermometer in a science lab displays the temperature in both Celsius and Fahrenheit. If the mercury in the thermometer rises to 56 degrees Fahrenheit, what is the corresponding Celsius termperature? And then they give us the two formulas - if we know the Celsius temperature, how do we figure out the Fahrenheit temperature, or if we know the Fahrenheit temperature how do we figure out the Celsius temperature. And these are actually derived from each other, and you'll learn more about that when you do algebra, and we also - maybe in another video - will explain how you do derive them, and this is kind of interesting, involves a little bit of algebra. But they gave us the formula, so they really just want us to apply it, and, maybe, make sure we understand which one we should apply. Well, they're giving us the Fahrenheit temperature here, so F is equal to 56, and they're asking us for the Celsius temperature, so we need to figure out what the Celsius temperature is. Well, in this one over here, if you know the Fahrenheit temperature you can solve for the Celsius termperature. So let's use this, right over here. Our Celsius temperature is going to be (5 / 9) times the Fahrenheit temperature. - the Fahrenheit temperature is 56 degrees Fahrenheit - minus 32. Well 56 minus 32 is 24, so this is going to be equal to (5 / 9) times 24, and this is the same thing as 5 times 24, all over 9. And before multiplying out 5 times 24 we can divide the numerator and the denominator by 3, so lets do that. If we divide the numerator and denominator by 3 we're not changing the value. 24 divided by 3 is 8, 9 divided by 3 is 3. So it becomes 5 times 8, which is 40, over 3, degrees. And if we want to write this as a number which makes a little bit more sense, in terms of temperature, lets divide 3 into 40 to get the number of degrees we have. 3 goes into 4 one time, with a remainder of 1, carry the 1 down and bring down the zero. 3 goes into 10 three times, with a remainder of 1, carry the 1 again, then you could bring down another zero - we now have a decimal point over here. 3 goes into ten 3 times, so this 3 is going to repeat forever. So you could view this as equal 13.333... - it'll just keep repeating, this line on top means repeating - degrees Celsius. Or, you could say that 3 goes into 40 13 times with a remainder of 1. So you could say that this is also equal to 13, remainder 1. So 13 and one third degrees Celsius. Either way it works, but that's our Celsius temperature when our Fahrenheit temperature is 56 degrees.