We met negative numbers on the number line. But where do they actually turn up? Everywhere there is a natural zero to measure from — and things can sit below it.

Zero is the reference point: "nothing", "ground level", "an empty balance". A negative number simply means below or less than that zero.

• Temperature. Zero is freezing point. A cold night of -4^\circ\text{C} is four degrees below freezing.
• Money. Zero is an empty account. A balance of -\pounds 20 means you owe \pounds 20 — a debt.
• Depth. Zero is sea level. A submarine at -30\,\text{m} is thirty metres below the sea.
• Floors. Zero is the ground floor. Floor -2 is two levels down in the basement.

In every case the minus sign answers one question: which side of zero are we on?

A thermometer is just a number line stood on its end. Press play: the temperature starts warm, then drops — the marker slides down the scale, crosses zero, and ends up below freezing. Each value is read aloud.