How does the position of a digit change its value in a place-value system?

In a positional numeral system, the value of a digit is determined by its specific position or place within a number. Each position corresponds to a power of the system's base ($b$), and the total value of the number is the sum of each digit multiplied by its respective place value.123

For any number $N$ represented in a base $b$, the value is expressed as:
$$N=a_n{b}^n+a_{n-1}{b}^{n-1}+\dots +a_{1}b+a_0$$
In this formula, each digit ($a$) is multiplied by the base raised to the power of its position. For example, in the decimal system (base 10), the digit "2" in "20" represents $2\times {10}^1$, while in "200" it represents $2\times {10}^2$.41

This system relies on the position to indicate the power of the base, which necessitates the use of a zero symbol to act as a placeholder for any powers of the base that are not present in the number.4