## Sunday, November 15, 2015

### Notes on the metric system

The United States uses a measurement system originated in Great Britain, which is sometimes called the Imperial system or the customary system. The relationships between measurements aren't very user friendly, and even Americans aren't very good at remembering all of them, according to tests I gave students at the beginning of classes years ago.

Here are some examples of the stuff you have to remember.

Length
12 inches = 1 foot
3 feet = 1 yard
5,280 feet = 1 mile

There are also odd measurements that very few people use any more, like rods, fathoms, furlong and nautical miles.

Volume

Of all the parts of the system This one makes some sense because the next biggest named measurement is almost always a factor of 2 away, either 2, 4 or 8 times bigger. Let's start with the fluid ounce (fl. oz.) as the basic unit.

8 fl. oz. = 1 cup (8 fl. oz.)
2 cups = 1 pint (16 fl. oz.)
2 pints = 1 quart (32. fl. oz.)
4 quarts = 1 gallon (128 fl. oz.)

Yay, powers of two! Unfortunately it breaks down as we get smaller than a fluid ounce.

2 tablespoons = 1 fl. oz.
3 teaspoons = 1 tablespoon

Another way in the system to measure volume is the cubic inch. This is not related nicely to the fluid ounce, as 1 cubic inch = 0.554413... fluid ounces.

Weight
16 ounces = 1 pound or lb.
2,000 lbs. = 1 ton

There are also little used units like a hundredweight (100 lbs.), a stone (14 lbs.) and a long hundredweight (8 stone or 112 lbs.). When we get smaller than an ounce, the standard is a grain. 7,000 grains is a pound, which means 437.5 grains is equal to an ounce.

The metric system

Unlike the customary system, which was thrown together over time, the metric system was made all at the same time, so length is related to volume and volume is related to weight using water as the standard thing we will weigh. All you need to learn for most measuring are three words and three prefixes for most stuff.

Length
The standard length unit is the meter or m. 10,000,000 meters is the distance from the equator to the North Pole.

The important prefixes here. For long distances that Americans would measure in miles, the metric system uses kilometers or km. Kilo means "1,000", so this is 1,000 meters.

For short distances Americans would measure in inches, the metric system uses centimeters or cm, which is 1/100 of a meter.

For even smaller lengths where Americans would use fractions of inches, the metric standard is a millimeter, which is 1/1000 meters.

Volume
The standard measurement for volume is the liter or L. It is based on a cube 1/10 or a meter (or 10 cm) on each side. The liter is just slightly larger than a quart.

When dealing with very large volumes, the unit is still the liter.

For smaller volumes, the standard unit is the milliliter or mL. This is a cube one centimeter on each side, so it is also also called a cubic centimeter or cc.

Weight
The basic unit of weight is a gram, which is the weight of a cc of water at about 4 degrees Celsius, or about 39.2 degrees Fahrenheit. The temperature was chosen as the lowest point where at normal pressure, water shows no sign of freezing.

The gram is very small, so when measuring things the customary system would measure in pounds, the metric system uses kilograms or kg. A kilogram is slightly more than 2 pounds, and for very heavy weights that Americans would measure in tons, the metric system users resort to metric tons, which are 1,000 kg. (technically, this would be a megagram, but this word is almost never used.)

As small as the gram is, some small measurements like medicine doses are doled out in milligrams or mg. When medicine is measured, not even Americans use ounces or grains, though when I was a kid, grains were used on aspirin packages. One gram is about 15 grains and sometimes there was confusion, leading to massive overdoses or underdoses.

Conversion values

We only need a single conversion number, and depending which direction the conversion is in, we either multiply by the conversion number or divide by it. Here is an example.

1 inch = 2.54 centimeters (cm)

If we have 40 inches, the 40 is related to the 1, so 40/1 = x/2.54. With fractions, we cross-multiply to get 40*2.54 = x*1, so x = 101.6 cm. If we are asked to round to the nearest whole number, it would be 102 cm.

If instead we have 40 cm, the fraction would be x/1 = 40/2.54 = 15.7480315... inches, which could round to 16 inches, 15.7 inches or 15.75 inches, depending on the level of rounding.

Here are some of the standard numbers used for conversion.

Length, middle distances: 1 meter = 3.2808 feet or 39.37 inches
Length, long distances: 1 kilometer = 0.6214 miles

Weight, small weights: 1 gram = 0.03527 ounces
Weight, medium weights: 1 kilogram = 35.27 ounces = 2.2046 pounds
Weight, large weights: 1 metric ton = 2,204.6 pounds = 1.1023 metric tons

Volume, small measures: 1 milliliter = 0.033814 fluid ounces
Volume, medium to large measures: 1 liter = 33.814 fluid ounces = 1.0567 quarts
Volume, liters to cubic inches or cubic feet: 1 liter = 61.0237 cubic inches = 0.0353 cubic feet