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### Decimal system

The decimal system uses the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for writing the decimal numbers.

##### Explanation

The number 237 is composed of

 2 × 100   = 2 × 102  3 × 10    = 3 × 101  7 × 1     = 7 × 100

You know that 100 is equal to 10 × 10 = 102 and you can write a 10 as 101, and a 1 like 100. If there are digits after decimal point this continues. The power decreases, reaches less than zero, which means it becomes negative. Thus 0,1 = 10–1. The number 4267,893 is composed of

 4 × 1000  = 2 × 103  2 × 100   = 2 × 102  6 × 10    = 6 × 101  7 × 1     = 7 × 100  8 × 0,1   = 8 × 10−1 9 × 0,01  = 9 × 10−2 3 × 0,001 = 3 × 10−3

Behind every digit in a number is a power of 10, that depends on its position. Because of that you must write a 0 if a certain place has no value. The number 3600,102 is composed of

 3 × 1000  = 3 × 103  6 × 100   = 6 × 102  1 × 0,1   = 1 × 10−1 2 × 0,001 = 2 × 10−3

Now we understand why  is

And we better understand the number 1, as

We have seen that numbers with a negative exponent are just fractions. You see it clearly in