Time to bring it together: decimals and negative numbers, in one tour of the number line.

Decimals, by zooming in

Eon's dad coded the mouse wheel to zoom the number line. Zoom between 0 and 1 and the decimals appear:

  • 0.46 is greater than 0 but less than 1 — it's in between.
  • 0.77 too. 1.5 sits between 1 and 2.

Keep zooming and you hit the program's limit, but in real math you could zoom forever — there's always another decimal in the gap.

Negatives: go left of zero

Now the new move — drag the marker to the left of zero, into the negative numbers: −1, −2, −2.45, and so on. These can be decimals too.

But negatives can feel confusing… until Eon's dad gives the picture that makes it click: a building.

The ground floor is 0. Go up: 1st floor, 2nd, 3rd — that's +1, +2, +3. Go down into the basement parking — B1, B2 — and that's −1, −2. Negative numbers are just the floors below the ground.

Dig deeper still — imagine a machine boring toward the center of the Earth — and you go more and more negative.

The tricky bit: which negative is bigger?

Because the "further right = bigger" rule never changes, negatives behave in a way that surprises everyone at first:

  • −9 vs −1: which is greater? −1! It sits further right (closer to the ground floor). As Eon's dad says, a big-looking number with a minus is actually really small.
  • The trickiest one — −5 vs −6: −5 is greater. Normally 6 beats 5, but the minus flips it: −5 is one floor above −6 in the basement.

Try it

Two basement levels: −3 and −8. Which is the higher floor (the greater number)? (−3 — it's closer to the ground, further right on the line.)