I admit it: I didn’t anticipate this is a sort of error when I wrote a book on learning the metric system. MSNBC made a huge one in a tweet where they converted Celsius to Fahrenheit. The MSNBC tweet says it all: “Latest UN report says humanity will warm planet by 2.7ºC or roughly 37º F.”
Now, if you’ve used the metric system and have some idea what a degree Celsius is like, you know three of them isn’t over 37 degrees Fahrenheit. And despite my low opinion of MSNBC, I really can’t say much because this is precisely the type of clumsy error that bit me time and again in school, and is all too easy to fall prey to even now. As such, it serves a good example of what a clumsy error is in math, and a bit about how it comes about.
First, lets’ run through how to convert from degrees to Fahrenheit. It’s really straight forward. First, we have to know that, at sea level, water freezes at 0º Celsius and 32º Fahrenheit, and boils at 100º Celsius and at 212º Fahrenheit. This means the number of degrees between the two points in Celsius is 100 – 0 = 100, and in Fahrenheit 212 – 32 = 180. So, 100 degrees C = 180 degrees F, which means 1 degree C = 180÷100 degrees F = 1.8 degrees F. In other words, degrees C x 1.8 = degrees F.
However, we need to do one more step to convert Celsius to Fahrenheit. Since 0 on the Celsius scale corresponds to 32 on the Fahrenheit scale, we need to shift the degrees Celsius upward by 32 after we multiply them by 1.8. This gives us the following equation: C x 1.8 + 32 = F. We can also solve the equation to convert from Fahrenheit: (F – 32) ÷1.8 = C.
Now that we have a conversion formula, it’s easy to transform Celsius to Fahrenheit. Let’s say the temperature is 20º Celsius. To convert it to Fahrenheit we follow the formula: 20 x 1.8 + 32 = F = 68º Fahrenheit. Simple.
Except that we need to keep in mind what the formula is doing. Looking at that MSNBC tweet, it gives the temperature increase as 2.7º C. What is it in Fahrenheit?
Now that we have a conversion formula, why not use that? 2.7 x 1.8 + 32 = 36.86, and rounding that to the nearest degree is 37º F, the same value that’s in the MSNBC tweet. It’s also, unfortunately, wrong.
Once you think about it, it’s easy to see. The UN report claims an increase of 2.7º C. So, whatever the base temperature is, the UN claims it will be 2.7º C more. If it happens to be, say, 14º C now, the UN claims it will be 14 + 2.7 = 16.7º C. However, our formula is designed to convert a reading in one scale to an equivalent in another. To mindlessly stick to the conversion formula, 14º C = 57.2º F; 16.7º C = 62.06º F; so the increase in Fahrenheit would be 62.06 – 57.2 = 4.86º F. Or we could just note that each degree Celsius is equal to 1.8 degree Fahrenheit, and multiply 2.7 by 1.8, which equals 4.86º Fahrenheit.
The main source of clumsy errors in math is being in such a hurry that you don’t think about what you are going. If you use an online converter or a conversion function on a calculator, like the equation it’s based on converting from one reading to another. When you’re in a hurry and don’t have a good feel for the units, it’s very easy to make a clumsy error just like MSNBC tweeted to the world. Just ask my old math teachers.
Having self-induced math anxiety (a long, shameful, story of laziness and keeping my mouth shut about having a teacher’s book with all the answers), I had a tendency to do slowly on tests, and I tried to compensate by hurrying through the answers. Then I’d end up with clumsy errors. That’s why it’s always a good idea for a team to check each other’s calculations, no matter how straight forward they seem. Because, just like on those tests and just like that MSNBC tweet, it’s all too easy not to think about what you’re doing. Nor is this restricted to word problems. Most of my clumsy errors were with computation, where the equation was already set up. Basically, clumsy errors result when you’re doing math on autopilot.
Knowing this, we can do things to help reduce our clumsy errors. For instance:
Double check your work, possibly using a different method. This helps check your reasoning.
Know the units you’re working in. Back in the early days of personal computers, when I wrote a program for work, a colleague said I’d come up with a great “dodge” because of the tendency to blindly accept information on a printout. He was right. This is particularly true if the output is just numbers to us. If we don’t have a feel for the units, we might not go “That doesn’t look right” when our calculations are off.
Take time to think. Thinking when doing calculations is like aiming at a target. It does no good to be fastest draw if you can’t hit your target. In the same way, it does no good to be the first to finish a test if you get all the answers wrong.
Above all, practice. Speed comes through experience. The more we practice, the faster we’re able to do the calculations correctly.
Will this eliminate all clumsy errors? Unfortunately not. Everyone gets brain fade every now and then. What it will do is help you make less of them, and help you catch them before turning in a test, or a report at work. There’s few things as embarrassing as having an error come up at a big presentation – unless it’s tweeting it to the entire world. Or, maybe, showing up in a blog post on clumsy errors.