Not only does the metric system make math easier in some areas, it also makes it harder in others!!!?

Question

Why does one cubic centimeter = 1 mililitre??? sure, mililitre sounds cooler than centilitre, but if you could convert from one cubic centimetre to one centilitre, it would save grade 8 kids from having to learn how to convert the units. 1 cubic meter could equal 1 litre, wouldn't life be great??? Didn't anyone ever think about that???

Answer 1

The problem is that, if we set one cubic centimetre to one centilitre, that would *not* work out to one cubic meter = 1 litre. In fact, it would work out to 1 cubic meter = 10,000 litre.

The reason? If you take a box that's 1 cm on a side -- 1cm x 1cm x 1cm -- and multiply each dimension by a factor of 10, you wind up multiplying your volume by a factor of 10x10x10 = 1000.

Since the scaling of cubic-length to volume doesn't proceed in a 1:1 ratio, instead the core units (metre, litre) were designed (1) to be reasonably close to other, commonly known measurements, to make estimating conversions easier, and (2) such that certain common arithmetic operations, like 1cc = 1mL, worked out cleanly.

Answer 2

cubic CENTImeters are MILLIlitres because you are moving from a 2 dimensional (distance) unit to a 3 dimensional (volume) unit.

the box containing 1 litre would have 10 centimeters on a side. So 100 for a 2 dimensional face. Now you expand that face into the 3rd dimension (creating volume) and you multiply by 10. So your face units (square centimeters) which were 1/100th of the total area now become 1/1000th of the volume. You multiplied by 10.
Centi-1/100th
Milli-1/1000th.
Makes pretty good sense to me!
No, it doesn't line up centi/centi, milli-milli, but that is just how it goes.

Just remember that all measuring systems are arbitrary. The only absolute units we can really use are days and years. And those are only relative to earth, and guess what? The length of a day is slowly changing!!

Any distance measurement will be arbitrarily picked by some human somewhere. Same with volume, time, etc...And since all other units are based off of these, the whole system is therefore arbitrary.

But at least you don't have to deal with the American/English crap system of miles, yards, feet, inches, ounces, pounds, tons, fathoms, leagues, acres, quarts, pints, cups, barrels, gallons, etc....

Answer 3

If one cubic meter did equal one liter of volume, then it still would not scale correctly as you are hoping, because then one cubic centimeter = 1/100^3 cubic meters = 1 millionth of a cubic meter. Whereas, one centiliter is still only 1/100 of a liter. The problem is that one measurement extends over three dimensions (hence, the ^3), while the other is a direct measure of volume in itself.

Why make the cubic centimeter and the milliliter equivalent? In short, practicality. The meter was originally chosen to be 1/10,000,000 of the distance from the equator to the north pole. And the liter was originally defined to be "one cubic decimeter". But why a cubic decimeter? So that a liter in itself can describe common volumes in practical terms, e.g. a bucket carrying a liter or two of water. (Had the definition instead been "one cubic meter", people would have been measuring their buckets not in liters, but in centiliters.) So aside from the original definition of "1 liter = 1 cubic decimeter", we also have the more common and useful equivalence of "1 milliliter = 1 cubic centimeter".

Did you also know that a third basic metric measurement, the gram, was also derived from the first two and tied together using the properties of a common fluid? One gram was originally defined as the weight of one cubic centimeter (or, of course, one milliliter) of water at its most dense temperature of about 4C.

The fourth basic metric measurement was derived on its own, but also based on water. The centigrade (or celsius) scale was defined by simply taking the freezing point and boiling point of water and dividing it into 100 gradations.

Answer 4

I was raised using the metric system and graduated in engineering... but this had never occurred to me. Yes, in the case of length and volume, there is not a direct relation between the basic units of the metric system, i.e. meter and liter.

However, this still would not solve your problem in fact it would be harder. If we had a basic unit of volume equal to a cubic meter (we can call it bliter, for big liter) a cubic centimeter would equal 0.000001 bliter. Now, cent means 1 hundredth and mili means 1 thousandth, so 1 cubic centimeter would not be 1 centibliter.

Answer 5

I think you are missing something in learning the metric system.

First, please remember that when you jump to 3 dimension things get larger.

You are forgetting all of the connections in metric.

1 liter(volume) of water = 1 kilogram(mass)
1 liter = 1000 cc or 0.001 cubic meter

A cubic meter of water would be 1000 kilos.

Use the website below for more help on weights and volumes.

Answer 6

I'm not sure there's really a non-rhetorical question in there, but here goes. I teach this stuff to teenagers and I think it's better the way it is for two reasons. One, the base units are properly sized for consumer use. Consumer products are most easily measured in liters (gasoline and wine in Europe), meters, and kilograms. Second reason, you'd still have odd calculations to do if you switched the system around, but the way it is you still have to opportunity to teach how to convert units. That's a very useful skill in scientific applications. I don't see having to bother with that as being necessarily a negative. Sure it makes things hard. But if we avoided hard things altogether no one would give birth.