Inline Notation
Sometimes a unit like $\u{mi\over hr}$ will be written with inline notation, like this: mi/hr. This is useful because it saves room (and it's hard to type fractions), but there are a few things we need to be careful of. First, remember that when a fraction appears in the denominator of another fraction, then the roles are reversed. For example, in $$5\u{kg\over m/s} = 5\u{kg}\u{s\over m} = 5\u{kg\cdot s\over m}$$ the seconds "s" is in the denominator of the the denominator, which means it really belongs in the numerator.A second thing to note is a common convention we use: if you see a number like $2\u{kg/m\cdot s}$, it is assumed that everything before the slash is in the numerator, and everything after the slash is in the denominator. So $$2\u{kg/m\cdot s} = 2\u{kg\over m\cdot s}$$ and not $2\u{kg\over m}\cdot s$. However, if there are two or more slashes, then that does not indicate a fraction-in-a-fraction. For example, $$2\u{kg/m/s} = 2\u{kg\over m\cdot s}$$ and not $2\u{kg/m\over s}$. Yes, this can be a little confusing! When handwriting units it's probably best to avoid this type of notation, but in typing it is so much easier than writing the traditional fraction that sometimes it's irresistible!
One other thing to point out: it is common to use exponents in units, like $$\u{s^2} = \u{s\cdot s}$$ The exponent only applies to the unit that it is attached to; for instance, \(\u{ms^2} = \u{m\cdot s\cdot s}\), and the meter is not squared. The exponent does, however, apply to any prefixes the units might have. (We talk about metric prefixes in Metric Prefixes.) Thus $\u{cm^2} = \u{cm\cdot cm}$. This is particularly important to remember when we work with area and volume.