# Is there any irrational number in decimal with a rational binary expansion?

According to this question, the binary expansion of any rational number is always either terminate or repeated. And there are some irrational numbers in decimal with an irrational binary representation. For instance let us consider $\sqrt {2}$.

$$\sqrt {2}=(1.41421356237309504880\dots)_{10}\\=(1.01101010000010011110…)_2$$

My question: Is there any irrational number in decimal with a ratinal binary expansion?

• That's not the definition of a rational, only a consequence. The definition is, a number is called "rational" if it equals an integer divided by another integer. This has nothing to do with base. – Akiva Weinberger Jun 26 '17 at 9:05