Video: Conversion between Degrees Celcius and Degrees Fahrenheit

The formula to convert from degrees Fahrenheit to degrees Celsius is given as 𝐹 = 1.8𝐶 + 32. Use the formula to convert 54 degrees Fahrenheit to degrees Celsius, giving your answer correct to one decimal place.

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Video Transcript

The formula to convert from degrees Fahrenheit to degrees Celsius is given as Fahrenheit equals one and eight tenths times Celsius plus 32. Use the formula to convert 54 degrees Fahrenheit to degrees Celsius, giving your answer correct to one decimal place.

We can start with the formula we were given. Fahrenheit equals 1.8 times the degree Celsius plus 32. We know that the value we’re trying to convert is 54 degrees Fahrenheit. Because we’re given Fahrenheit, the 54 must be plugged in for the 𝐹. The Fahrenheit degrees equals 1.8 times the degrees Celsius plus 32.

To find Celsius, we’ll need to isolate it; we’ll need to get it by itself. We do that by subtracting 32 from both sides of our equation to keep it balanced. 32 minus 32 equals zero; 54 minus 32 equals 22. We’re left with 22 equals 1.8 times Celsius plus zero. 22 equals 1.8 times 𝐶. That means that 1.8 times some number equals 22.

We need to know what that missing value is. We find that value by dividing 22 by 1.8. Our divisor in a division problem can’t have a decimal place. So we move the decimal place one to the right. And we do the same thing for the dividend, adding a zero and moving the decimal place.

Now we’ll divide 18 by 220. 18 goes into 22 one time. One times 18 equals 18. We need to subtract 18 from 22. We can’t take eight from two, so we borrow from our hundreds place. Now we’re subtracting eight from 12, which equals four. One minus one equals zero. After that, we bring down our zero, and we ask how many times does 18 go into 40. 18 goes into 40 two times. When we multiply 18 by two, we get 36. 40 minus 36 equals four.

We recognize that we have a remainder here. So we add a decimal place and an additional zero and bring that zero down. We have the same problem. We’re asking how many times does 18 go into 40: two times. 18 times two is 36. 40 minus 36 equals four. We add a zero. Bring it down. We have 40 again. We ask how many times does 18 go into 40: two times. Two times 18 equals 36.

What we see here is that, over and over again, we’re going to get a two repeating. No matter how many times we divide and add a zero, we just keep getting two. Thankfully, our instructions tell us we only need it correct to one decimal place.

If we’re rounding to one decimal place, we’re rounding to the nearest tenth. The two in the hundredths place tells us we need to round down. 12.22 would round to 12.2. Okay, now we have 12.2, but what’s happening here? What does this 12.2 mean? Well, we’ve divided 22 by 1.8, and what we find is equal to the degrees Celsius. 54 degrees Fahrenheit is equal to 12 and two tenths degrees Celsius.

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