Ordering Both Kinds

Which is bigger, $\frac{2}{5}$ or $0.3$? A fraction and a decimal are hard to compare as they stand, so write them in the same kind first. Turning the fraction into a decimal is usually quickest: $\frac{2}{5}$ is 0.4, and 0.4 is bigger than 0.3. So $0.3$ $\lt$ $\frac{2}{5}$.

2/5 is 0.4, so it sits just right of 0.3.

The same idea orders a whole list. To put $0.7$, $\frac{5}{8}$ and $\frac{3}{5}$ in order, write each as a decimal: 0.7, 0.625 and 0.6. Now the order is plain: $\frac{3}{5}$, then $\frac{5}{8}$, then $0.7$. On a number line from 0 to 1, a value's decimal tells you how far along the line it sits.