Decimal system

The decimal system has a base 10 and is represented by the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. The name used for each of the symbols is digit

When we combine several digits, we have a number. Their value depends not only on the value of each one of them, but on the position they have within their group

The passage of any number to base 10, would correspond to applying the formula:

b_1\cdot 10^{(n-1)}+\cdots+b_n\cdot 10^0

Where n would be the length of the string, and b_i, the value corresponding to the i-th position of the string, starting from left to right

Example: Representation of the number 3737 in decimal system

3737=3\cdot 10^3+7\cdot 10^2+3\cdot 10^1+3\cdot 10^0

Representation with decimal

If the number also has decimals, it will be expressed with the following formula:

b_1\cdot 10^{(n-1)}+\cdots+b_n\cdot 10^0+b_{n+1}\cdot 10^{-1}+\cdots+b_{n+m}\cdot 10^{-m}

Where n would be the length of the string without decimals, m the length of the string with decimals, b_i, the value corresponding to the i-th position of the string, starting from left to right

Example: Representation of the number 56.34 in decimal system

56,34=5\cdot 10^1+6\cdot 10^0+3\cdot 10^{-1}+4\cdot 10{-2}