how does the metric system work?
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There is a certain length that we call a meter. It is defined as the distance that light travels in vacuum in a given time (1/299792458 s).
Every fraction of 10 and every multiple of 10, the unit gets a different prefix, but not all prefixes are commonly used.
So, a tenth of a meter is a decimeter, but that is rarely used. The same length is more commonly referred to as 10 centimeters (1 cm=1/100m).
10 meters are a decameter, 100 meters are a hectometer, but those units are rarely used. 1000 meters is a kilometer, which is a common unit.
Also litre (l), also spelled liter is a unit of volume in the metric system, equal to one cubic decimetre (0.001 cubic metre). From 1901 to 1964 the litre was defined as the volume of one kilogram of pure water at 4 °C (39.2 °F) and standard atmospheric pressure; in 1964 the original, present value was reinstated. One litre is equivalent to approximately 1.0567 U.S. quart.
[Source](https://www.britannica.com/science/litre)
A calorie is broadly defined as the amount of energy needed to increase the temperature of 1 gram of water by 1 °C (or 1 K, which is the same increment, a gradation of one percent of the interval between the melting point and the boiling point of water)
[Source](https://en.m.wikipedia.org/wiki/Calorie)
What part of the metric system is it you need explained?
The metric system or the “International System of Units” as it is formally known is a System of units used throughout the world. (The units are also know as **SI-Units** because French abbreviations tend to be backwards compared to English ones.)
It replaced older systems used in Europe where every country and sometimes every large city had their own system of weights and measures. It used to that there were dozen of different types of pounds and feet and everyone’s miles and tons had different amounts of their pounds and feet.
Some of that confusion lives on with for example Gold being measured in different ounces and pounds than other stuff. regular US pounds have 16 regular US ounces but gold is measured in troy pound and troy ounces where there are 12 troy ounce to the troy pound.
Also American tons are different from British imperial tons despite the pounds being the same.
The confusion was quite a lot worse in ages past when every city had their own units, everyone measured things differently and nothing matched up.
During the age of enlightenment and with the background of the french revolution new units were created that should get rid of the confusion of all the old ones.
One important thing is that instead of of going with larger and smaller unit totally disconnected from each other, for every thing that was measured some base unit was created and larger and smaller units were created by adding the same prefixes. all those prefixes were powers of 10 and mostly powers of 1000.
So you did no longer have to memorize how many foot there were in a mile or how many pounds in a hundredweight.
All you needed to know was that kilo- meant thousand and you instantly knew that a kilometer was 1000 meter and a kilogram was 1000 gram and a kilojoule was 1000 joule etc.
This also made conversion between units easier as you did not have to do any actual math.
How many kilometer are 1609 meter?
1.609 km
No math necessary you just need to move the decimal point left or right a bit.
(Time and angles are the exception. There was an attempt to decimalize time and decimal angle measures exist, but we still use a 24 hour day today with each hour having 60 minutes and 60 seconds. Milliseconds however are a thing. similarly circles are divided into 360 degrees and each degree into 60 minutes and each minute of an arc into 60 seconds. tradition won out there)
The other advantage was that you get from one unit to the other by multiplying or dividing by full units.
Power for example is mass times area divided by time cubed.
If you were asked how many pound square inches per cubic fortnight you would need to get a single horsepower, not even people who use those units would be able to easily tell you of the top of their head.
In SI units 1 Watt is simply 1 Kg times a square meter divided by a second cubed.
All commonly used electrical unit like Volt and Ohm etc are actually metric units this way.
Doing any sort of physics math without SI units get unnecessarily complicated very fast.
The basic ideas is to have 7 base unit and lots of derived units. Standard prefixes for powers of 10. This means that you can easily combine quantities by simple multiplication/division without conversion constants.
My favourite: A4 is 1/16th of a square metre. So an A4 sheet of 80g/m^2 paper weighs exactly 5 grams. Useful when figuring out postage.
Also: 10 mm of rain means 10L/m^2 . And 1 inch of rain is 5.61 gallons per square yard. Those conversions are all simple in metric.
It’s all about the number 10.
We like to count in 10s because we have 10 fingers. The way we write numbers reflects this: you count 1, 2, 3… all the way up to 9, then you write a “1” for your first 10 and then start again with the next digit: 11, 12, 13… etc.
That’s all great, until you start to measure things in numbers that aren’t 10. There are 16 oz in a lb, so what’s 331 oz in lb? Our number system counts things in 10s, not 16s, so that’s hard to do.
Just imagine how much easier life would be if there were 10 oz in each lb, you’d just divide that 331 oz by 10 to get 33.1 lb.
Also, it’s a hassle remembering how many oz there are in a lb. Is it 14, or 16? Or was that pints in a gallon? And do I mean imperial gallon, a US liquid gallon, or a US dry gallon (all of which are different)? Wouldn’t it be nice if there was a consistent number of small things in a big thing: like just 10 oz in a lb and *also* 10 pints in a gallon?
That’s precisely what the metric system does: bigger units are multiples of ten of smaller units, and that’s consistent across all the measurements. Normally the little units are 1000x smaller than the big ones, but the names explicitly tell you that (i.e. “milli” = thousandth, “kilo” = thousand):
1000 mm = 1 m (metres, lenght)
1000 ml = 1 l (litres, volume)
1000 g = 1 kg (Kilograms, mass)
There’s another benefit, which is that many of the units are related. If I asked you precisely how many gallon jugs 32 lb of water would fill that would be tricky, but it’s easy to tell you how many litre bottles 32 kg of water would fill: it’s 32 (because 1 l is the volume of 1 kg of water).
There are a few key principles of the metric system.
It starts with “base units.” It takes what are thought of as the core physics concepts – time, length, mass, electric current, thermodynamic temperature, amount of substance, luminous density – and assigns each of them a unit ([these days each defined in relation to one or more core constants](https://en.wikipedia.org/wiki/File:Unit_relations_in_the_new_SI.svg) and each other).
All other units are derived from and defined in terms of those base units, and must be ‘coherent’ – meaning that there are no scale factors involved. For example, once we have the metre for length and the second for time, we get the unit for acceleration as the metre-per-second-squared. Once we have acceleration and mass, we have the definition of force as mass multiplied by acceleration, so our unit for force (the Newton) must be the unit for mass multiplied by the unit for acceleration (1N = 1 kg * 1m/s^(2)). Now we have the Newton for force, we have energy defined as a force multiplied by distance, so our unit for energy (the Joule) must be 1 Newton * 1 metre. And so on.
The other useful principle is that we have a system of pre-fixes for getting different orders of magnitude. If you look at, for example, the [traditional English units for length](https://upload.wikimedia.org/wikipedia/commons/9/9e/English_Length_Units_Graph.svg), even with just the simple ones you have 12 inches in a foot, 3 feet in a yard, 1760 yards in a mile. You have 2 yards in a fathom, and 8 furlongs in a mile. Each of these has a different conversion factor, and a seemingly random name. The metric system works on powers of ten; you have the metre, the kilometre (1000m), the centimetre (1/100m), the millimetre (1/1000m) and so on. Given any unit you can get another by multiplying by or dividing by 1000, and changing the prefix to the next one.
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