## Thinking Mathematically (6th Edition)

A symbol for zero is always needed in positional system because when it includes in expanded form, the expanded form will look more clearly. For example, the expanded form $\left( 2\times {{10}^{3}} \right)+\left( 1\times 1 \right)$ will be seen clear when it will have written as from $\left( 2\times {{10}^{3}} \right)+\left( 0\times {{10}^{2}} \right)+\left( 0\times 10 \right)+\left( 1\times 1 \right)$.