proof: upper bound error of approximating a number with only $n$ decimals precision

Question

Suppose you have a real number $A$ and approximate it by only $n$ decimal places. Call this number $a$. proof that the upper bound of absolute error of this approximation $|A-a| \le 5 \times 10^{-(n+1)}$.

Can anyone help me to solve this theorem? I thought that i can use induction technique but it doesn't work.

Answer 1

What is the distance between two neighboring numbers with $n$ decimal places? $A$ is no more than half that from the nearest one.