How does the decimal system use powers of 10 to represent a number?

The decimal system is a positional numeral system that uses 10 as its base. In this scheme, the value of each digit is determined by its position, which corresponds to a specific power of 10.12

Any number $N$ can be expressed as a sum of digits multiplied by powers of 10, represented by the formula:
$N=a_n{10}^n+a_{n-1}{10}^{n-1}+\dots +a_1{10}^1+a_0{10}^0+a_{-1}{10}^{-1}+\dots$

For example, the number 543.21 is calculated as the sum of its positional values:13
$(5\times {10}^2)+(4\times {10}^1)+(3\times {10}^0)+(2\times {10}^{-1})+(1\times {10}^{-2})$

In this system, the position of a digit indicates the power of 10 by which it is multiplied. Moving to the left of the decimal point increases the power of 10, while moving to the right decreases it. This positional structure allows for the representation of any number using only ten unique digits (0–9) and a decimal point to denote fractions.123