Different number systems are used quite a lot, especially in computer science. In this case, the number systems mainly used are base 2, base 16 and of course base 10.
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It is nine and six tenths. To get deeper into the "meaning" of a number you would need to study Dedekind's work. This site is not best suited for that.
The reason you have to study the real number system is because it is so applicable in the real world. It is one of those concepts that you can use outside of school when counting change in your pocket when you are at the grocery store, or deciding how much you of an ingredient you need.
Do all your homework and study for tests. If you feel that you are having trouble learning math you may need to be tested for a learning disability. Having a learning disability doesn't mean you are not smart, nor does it mean you aren't trying hard enough. It means you will need a different method to learn or sometimes to even understand the concept. A math tutor can help you study but if you have a LD you may need a math specialist. Talk to your teacher about where to get help.
That really depends in what you want to work in the future. If you want to study some engineering field, you'll need LOTS of math. If you want to teach in schools or colleges, you may well require SOME math. For many other areas, you'll need only very basic math knowledge.
Oh, dude, math time! So, if 10,000 is 10% of a number, you just need to divide 10,000 by 0.10 to find out what that number is. That number would be 100,000. Boom, math wizardry at its finest!