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- 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.