There are several advantages. Some of them are:
1. They are internationally agreed as standard. Not like a gallon which can mean one amount in the US and another in the UK.
2. Orders of magnitude for the same measure are related by simple decimal conversions and only a handful of prefices are required (although there are a lot more). By way of contrast, the Imperial system uses:
and so on, and on and on. The decimal structure also makes it very simple to use scientific notation for small and large quantities.
3. It is used by most people in the world. The main recalcitrant countries are USA, Liberia and Myanmar. Even in the US, scientists normally use SI. When they don't they have disasters like the one that trashed NASA's Mars Climate Orbiter!
4. There are many simple relations from measures for one characteristic to another. For example, the SI unit of length is 1 metre. 100 square metres = 1 are, the unit for area. 1 cubic metre = 1000 litres, the unit for volume.
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Yes, it is recommended because the SI-units are based on the metric system.
they aren't!
The standard for science the world over is the metric system, and most commonly the mks system of units. This stands for meter, kilogram, seconds. Different sub-fields may use slightly tweeked units like the cgs system which stands for centimeter, gram, seconds but these are still metric units.
It is a more logical system, where everything is divisible by 10. With other units, everything is arbitrary.
Metric units include millimeters, centimeters, decimeters, and meters.