rational numbers - How can I explain $0.999ldots=1$?

I have to explain $0.999\ldots=1$ to people who don't know limit.

How can I explain $0.999\ldots=1$?

The common procedure is as follows

$$\begin{align} x&=0.999\ldots\\ 10x&=9.999\ldots \end{align}$$

$9x=9$ so $x=1$.

Answer

What I always find the most simple explanation is:

$$\frac{1}{3} = 0.333\ldots \quad \Longrightarrow \quad 1 = 3 \cdot \frac{1}{3} = 3 \cdot 0.333\ldots = 0.999\ldots$$