# Gifted and bored

\(\)N is in Year 5.

“What are you doing at school now?”

“Umm, we are still converting fractions to decimals and back”

“Show me an example”

“Well, it’s something like \( \mathrm{\frac{1}{2}=0.5}\), \( \mathrm{\frac{1}{4}=0.25}\), \( \mathrm{ \frac{7}{10}=0.7}\) ”

“I see. Can you write \( \mathrm{\frac{1}{8 }}\) and \( \mathrm{\frac{3}{40 }}\) as decimals?”

He can. Without much effort.

“The interesting thing is that some numbers cannot be written as fractions, and as decimals they are infinitely long. Have you heard about a number called \( \pi\)?”

“Yes, I have. It’s very big, isn’t it?”

“No, the number itself is not big, it’s just a little over 3. But if you try to write it down, it looks like this: 3.141592653589793… The decimal tail is infinite, and there is no way to write it down as a fraction. That’s why we use either approximations like 3.14 or the Greek letter \( \pi\) to represent the number.”

“And what goes after …9793…?”

“I don’t remember the digits that follow, but you can easily find millions of digits online.”

“Wow… So”, he pauses, “why are we doing this”, he points at the piece of paper with \( \mathrm{\frac{1}{8 }}\) written on it, “if there is something like that in the world?” His finger moves along the chain of digits of \( \pi\).

Why, indeed.