[Numbers: First of all the metric/decimal system seems to make sense because we have a decimal number system. This probably originated because humans have ten fingers on which to count. If we had 8 fingers we'd probably have an octal system. If we had flippers we'd have a binary system, etc. Some time around junior high school we have learned all the arithmetic there is to learn. (Arithmetic deals with numbers mathematics deals with concepts.) First we learn to count, then to add, after that we learn multiplication tables of one and sometimes two digit integers. With this knowledge we can multiply larger numbers and we can do fractions. Addition, subtraction, multiplication and division of fractions involves nothing more complicated than multiplication and division of integers. It is only when we get to long division that we are forced to do decimals.
Stuff: Systems of measurement are not abstract concepts, but ways of dealing with stuff. Stuff is so many inches long; we have so many liters or pounds of stuff. So systems of measurement are really about what we need to do with that stuff in the real world. This determines the accuracy we need. The lower limit of accuracy is how precise we need to be. For the carpenter this is about a mm or 1/16 sometimes 1/32 inch. For the machinist this is decimal mm or .001 inch. For the surveyor this is .1 foot. (Aha, decimals are not limited to the metric system!) But there is also an upper limit on what we need to measure. Tape measures longer than 30 feet are specialty tools. If we are making a journey of several kilometers (or kilometres; with two spellings and two pronunciation so much for metric consistency) we probably don't need meters. So why measure stuff? I measure stuff so I can cut or modify it, combine it or add to it, or divide it. Somewhere in this process I need to commit figures to working memory. With US units I can do almost any manipulation in my head without use of a calculator.
Example 1. What is (4' 4 7/16â€)/3 ? The process is this: 4'/3 is 1' plus 12â€/3 = 1' 4â€. Then 4â€/3 is 1â€ plus 1/3â€. So I have 1' 5 1/3â€. Now my accuracy is 1/16â€ so 1/3â€ is 5/15â€ which I round of to 5/16â€. 7/16â€/3 is approx. 2/16â€ So 5/16â€ plus 2/16â€ = 2/16â€ = 7/16â€. Answer 1' 5 7/16â€. I've just done that in my head to a 1/16â€ accuracy!
Within the US system we seldom use more than 2 units at a time. We wouldn't often talk about yards, feet, and inches or quarts, pints, cups and ounces. The smaller units are always fractions of the larger units.
Example 2. What is one fifth of 2 quarts 4 Â½ ounces. The process is this: 2 qt. = 64 oz.
Divided by 5 that's 12 4/5 oz. 4 Â½ oz. is 9/2 oz. Divided by 5 that's 9/10 oz. 12 4/5 oz. Is 12 8/10 oz. Add 9/10 oz. = 12 17/10 oz = 13 7/10 oz. So 7/10 oz = 21/30 oz = approx. 20/32 oz. = 5/8 oz. So the answer is 13 5/8 oz. Doing this in my head I'm off by only .075 oz!
I can't do decimal long division in my head.
Three and powers of two: Usually I manipulate stuff in powers of two, repeatedly doubling it or dividing it. I do this most easily with integer units or fractions which are expressed in integers. I divide or multiply by three much more often than by five or ten. Which brings this discussion to the number 12 (= 2x2x3 = 2x6 = 3x4) often a more useful number than 10.
Units that seem arbitrary may not be. 1 mile = 1760 yards = 5280 feet. This makes more sense when you think that 1/2 mile is 880 yards; Â¼ mile is 440 yards (Remember that from track.); 1/8 mile is 110 yards; 1/16 mile is 55 yards. 1/3 mile is 1760 feet. 1/12 mile is 440 feet etc.
1 foot is 12 inches which can be divided by 3 and repeatedly by 2 when we allow fractions of an inch.
2 tablespoons = 1 ounce. 8 ounces = a cup. 2 cups = 1 pint. 2 pints = 1 quart. 4 quarts = 1 gallon. When you throw in a teaspoon you have thirds as well.
Ounces and pounds are powers of 2.
Often in the US system only one unit is used at a time; smaller quantities are expressed as fractions of that unit.
Human Scale: The metric system represents a dehumanization of measurement. An inch is based on the human finger, a foot on the foot, a yard on an arm or a pace. I can pace off yards but not meters. A meter was one ten-millionth of the distance from the pole to the equator, but is now the distance traveled by light in a vacuum in 1/299,792,458 second. I sure can't relate to that. Metric volumes relate to the meter. Metric weights relate to volumes of water. Metric temperatures relate to boiling and freezing water. Fahrenheit temperatures relate to the normal limits of human experience. Temperatures below zero or above 100 are extremes. Human sensitivity to temperature is so acute that it needs fractions of a metric degree.
We can use both: I cook a lot. I use both metric and US units. The difference between a quart and a liter is negligible. I like metric weights. My scale can use either. Metric translation of US recipes almost always use grams and milliliters; recipes from metric countries use more humanized units. Spanish cookbooks for instance use 3 kinds of spoons, soup spoons, dessert spoons, and coffee spoons. Metric liquor bottles come in two different regional sizes 750ml or 75cl. (My American English spell-checker likes750ml but not 75cl???)
I never met a dope dealer who couldn't instantly convert between metric and US weights.
Enough of my nonsense.