Google Calculator: Celsius Degrees and Square Dollars

In the past few days, I've seen images from Google calculator pop up on MathFail.com, as well as on digg, reddit and elsewhere. The image shows the following equation:

(0 degrees Celsius) + (0 degrees Celsius) = 273.15 degrees Celsius

Cut and paste the left side of the equation into Google if you don't believe it. Done? Okay.

While this might seem outrageous at first, it isn't the answer that's incorrect. It's the question. Google's calculator tried to parse it the best that it could.

Try either one of these and see what you get:
(0 degrees Celsius) + (0 Celsius degrees)
(0 Celsius degrees) + (0 Celsius degrees)

See the difference. The calculator does, too. One Celsius degree is not the same as one degree Celsius. The former is a unit of temperature; the latter is an actual temperature reading.

The first equation represents two positions on a scale. Those positions could just as well be named New York City and St. Louis. You couldn't add those two values together. However, if they had values on that scale, you could subtract them to find a displacement; i.e., how far apart they are. And the original equation could be changed to subtraction and yield a correct answer.

This brings me to a tip that I give my students, usually when reviewing percents (sales tax) and Order of Operations. I tell them that you can add dollar amounts, subtract them, or even divide them (in which case, have them notice that they lost the dollar sign and have them explain that back to me). However, if you ever find yourself multiplying two dollar amounts. Stop! You're most likely doing something wrong.

Which brings me to this graphic that I created, using Google's calculator:


What are square dollars? That's silly! Our dollars are rectangles.