This is the lesson where Eon's dad says, "This is a hard one" — and he's right. It's also where the number line gets a thousand times more interesting.
The line is secretly crowded
So far the number line had neat stops: 0, 1, 2, 3. But zoom in and… it's not just those points. Between them are lots of tiny places — like a ruler that has little marks between the big numbers. The "snap" mode was hiding them; turn it off and the marker can stop anywhere.
The impossible-sounding question
Eon's dad points to the spot exactly in the middle of 1 and 2 and asks: what do we call that place? It can't be 3 (that's further right). It needs its own name.
So he does something sneaky and smart — he names it with a letter, E (for Eon), as a stand-in:
- Is 1 less than E? Yes — E is to the right of 1, so 1 < E.
- Is E less than 2? Yes — E < 2.
So E sits between 1 and 2 (1 < E < 2). Then comes the reveal: that middle place has a real name — 1.5 — a decimal. Cut the gap in half, and 1.5 is the answer.
The mind-bending part: it never ends
Here's what makes Eon shout. Between 1 and 2 you found 1.5. But between 1 and 1.5 there's another number… and between those two, another… and another.
No matter how far you zoom in, there's always one more number in the gap. The numbers between 1 and 2 are countless — Eon's dad calls it "unlimited, like unlimited life."
That's the secret of decimals: 1.1, 1.2, 1.3… 1.45… 1.999 — you can always add another digit to point at a finer place.
A bonus you've seen before
Ever notice game or app updates like version 1.0.1? Eon's dad points out that's decimals at work — a tiny number added on the end to mark a small step forward. Same idea.
Try it
Name a number between 1.5 and 1.6. (Try 1.55 — and between 1.55 and 1.56 there's another one. They never run out!)