Irrational Numbers on the Number Line

An irrational number cannot be written as $\frac{p}{q}$ where p and q are integers and q is non-zero. Numbers like $\sqrt{2}$, $\sqrt{3}$ and $\pi$ are irrational because their decimal expansions never end and never repeat. The lab shows $\sqrt{n}$ for any positive integer n you pick.

Slide n from 0 to 50 and the lab marks $\sqrt{n}$ on the number line. Try n = 2 to see roughly 1.414, n = 9 to see exactly 3, and n = 17 to see an irrational between 4 and 5. Compare perfect squares against non-square n.

Students often write $\sqrt{2} = 1.41$ and stop, treating it as rational. Always mark $\sqrt{2}$ with a bar or write it as a surd in your final answer. Rounding too early loses marks in board questions asking for exact form.

The diagonal of a square floor tile of side 1 metre is $\sqrt{2}$ metres long. The ratio of any circle's circumference to its diameter is $\pi$, useful when buying lace to trim a round tablecloth. These lengths cannot be measured exactly with a ruler.