Ordering Both Kinds

Which is bigger, 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: 2/5 is 0.4, and 0.4 is bigger than 0.3. So 0.3 < 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, 5/8 and 3/5 in order, write each as a decimal: 0.7, 0.625 and 0.6. Now the order is plain: 3/5, then 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.