Question

Dear Mitch, 

I'm in 7th grade math even though I'm only in 6th grade.  (They moved me up a year for math after we took some test).

Anyway, I live in one of the states that starts school at the beginning of August, and so we've already been going for two weeks.  Here's my question:  In math she gave us a bunch of questions to answer and said we could use either the metric system or the regular one when we write our answers and we could get full credit either way.  So for one question the answer was two and a half meters, which is what I wrote down in the blank.  AND SHE MARKED IT WRONG WITH ONE OF HER BIG CIRCLES AROUND IT!?!? 

So when I asked her how it could be wrong when I checked it by plugging it back into the question, she said that THAT would be a little homework assignment for me, to do some research and find out how an answer could be wrong even though it checks out perfect. 

So you are my research.  What's up with the right answer being marked wrong?

If you could get back to me pretty soon, that would be awesome, thank you.

From Rich C.

Answer

Dear Rich,

Excellent question!  

Honestly, I always hoped someone would ask about this because I often hear people say things like "half a meter" or "three-quarters of a kilometer" or "half a centimeter", and I am always interested to note how readily these phrases are accepted in response.  "Just go another two, or two-and-half kilometers up the road," a helpful pedestrian once told me when I asked him for directions, "and you'll see the entrance..."

I thanked the person for giving me such a precise answer, and waved goodbye as I drove off to my destination.  BUT --  technically -- in the world of mathematics and mathematical communication, what that helpful person said is considered bad form.

 Of course, when a driver or pedestrian is giving or receiving directions, anything helpful – slang, or even slang to communicate he has no idea -- is great. In fact, when one is lost, any correct information is a gift.  BUT, as an answer on a math test in school, teachers have every right to expect from students a higher level of precision and correct mathematical grammar.  Listen: FRACTIONS AND THE METRIC SYSTEM DO NOT GO TOGETHER. 

So, although it is correct to say two-and-a-half miles, or two-and-a-half yards, or two-and-a-half feet or inches, it is NOT correct to say two-and-a-half meters or two-and-a-half centimeters or millimeters, etc.  

Why? 

Because the whole point of the metric system (or at least one of its big points) is that a person should be able to tell the degree of accuracy by the unit being used. 

What????

You see, the metric system, which is indeed the international system of measurement for scientists, serves a number of purposes.  And each of the purposes is considered to be one of the system's advantages over what you referred to as "the regular system".

Sometimes scientists are able to measure microscopic organisms, and a colleague reading the results of their research should be able to tell at a glance the form of measurement or magnitude of the evidence reported. 

QUESTION:  So what is a person supposed to do when he does all the calculations and the answer turns out to be two-and-a-half meters? 

ANSWER:  The person is supposed to change units, actually shift to the next unit down in size, and convert the quantity to the appropriate number of WHOLE units.  So, since there are 100 centimeters in one meter, there are fifty centimeters in half of a meter.  

So two-and-a-half meters are 250 centimeters.  And that would be the metric answer your teacher would like to see.  And I would agree with her.

Now... that said, there is an interesting footnote to this whole metric discussion, which is really another question: 

Why HASN'T the metric system taken off in the way it was supposed to -- completely replacing the "customary" system? 

Well, you are too young to know the history behind the answer to this first-hand, but there was a time in the United States, a few decades ago, when the government and educational system spent MILLIONS and MILLIONS of dollars producing materials to help the citizens transition once and for all times to the metric system and leave our traditional system of units to fade into oblivion.  The idea was that – eventually—inches, feet, yards, miles, pounds, ounces, etc., would become the next dodo birds of measurement.  (EXTINCT.)   Teachers were intentionally frightened by educational consultants, and those teachers did what they could to frighten students into believing that if they did not get their minds to make the switch they would be left behind in society, sort of the way someone who never learns to read may be left feeling he/she is in the dark about all kinds of information. 

It did not happen. 

The government and schools eventually gave up, though of course they continue to this day to stress the importance of knowing as much as reasonably possible about the metric system, and it is taught from the early grades up through the last moment of mathematical education -- as it should. In today's global economy, and the increasing coziness of the world produced by the World Wide Web, a.k.a. the Internet, a common language is a major part of successful communication. 

Indeed, most European nations as well as most nations in the rest of the world use the metric system, as do American businesses for international trade. When making deals with other nations, it is important that the people use a common system so all parties understand what is being transferred, etc. 

So... Why HASN'T the metric system REPLACED all other systems in every way? 

AND, MORE INTERESTINGLY, WHY HAVE NATIONS THAT USE THE METRIC SYSTEM DEVELOPED ALL SORTS OF VARIATIONS ON THE STANDARD UNITS? 

What was that?

Here:  In certain European countries, a person can buy a liter of drinking water, but he can also buy a 'country liter' or a 'folk liter' or even a 'half-liter'.  Why?

 The answer is that despite the precision of any particular system that scientists and merchants use, most people's minds work in a way that cannot be reduced to particular units just because someone else feels the desired units are superior.  There are certain things inherent in the way people think and visualize and imagine and recollect, and many of these uniquely human ways are more similar among different people than one might guess.  EXAMPLE:  When a person is thirsty and goes into a store to purchase a bottle of water, there is a natural unconscious impulse to seek out a certain amount of water, which may be packaged in a certain sized container.  The mind doesn't tell the stomach:  "Okay, now we really need one liter of water."

No, the process goes the other way:  The stomach tells the mind: "I am THIS thirsty," as a vague non-visual idea of the quantity forms in the mind. 

Then other factors come into the mix:  The mind and shoulders communicate and recognize that a huge jug of water will be a hindrance and an unnecessary drain of energy to carry home, even if by then half the contents will be consumed. There is an unconscious feeling of disequilibrium that most people feel at the notion of purchasing a large jug and pouring half of what was paid for out onto the ground before beginning the journey home with the remaining liquid.  And purchasing several of the smaller size to carry along the way usually doesn't feel as satisfying as grasping the one perfect size that you desire. And so all kinds of hybrid units have sprung up. Just as people in the U.S. often speak of five "city blocks" or "a country mile", there are a number of places in Europe and elsewhere that sell bottled water in sizes that satisfy people's stomachs, minds and budgets.  And since no metric unit (or any other unit) matches it perfectly, along with its creation comes a new name, such as the "athlete's liter", or the "family-sized liter".

So there you have it.  As usual, I did my best to answer your question, and then I kept going to make sure there would be more information than you requested – but, I hope, presented simply enough to engage you more than you expected!

Hope this helps, 

Mitch