It's often a good idea to leave units in your problem description
until you're sure they match up on opposite sides of each equation.
This can help you avoid mismatches, e.g.,
Q: A cylinder has a radius of 6 inches and a height of 50 centimeters.
What is the volume of the cylinder?
A: The formula for the volume of a cylinder is
V = pi * r^2 * h
If we just plug in our numbers, keeping the original units, we get
V = pi * (6 in)^2 * (50 cm)
= pi * 36 in^2 * 50 cm
= pi * 1800 in^2-cm
That _is_ a volume, but it's customary to use a single unit
of length when expressing areas and volumes. So in this case,
we'd want to convert inches to centimeters, or vice versa:
V = pi * (6 in * 2.54cm/in)^2 * (50 cm)
= pi * (6 * 2.54 cm)^2 * (50 cm)
= ... cm^3
More importantly, it can help you catch errors in translating
problem descriptions to equations. For example, given a question
it's common for students to jump in with an equation like
I have 15 coins in a bank, consisting of nickels and dimes. If the
total money in the bank is $1.15, how many kinds of each type of coin
do I have?
without really knowing whether it's correct. Being clear about
units can make a big difference:
d + n = 1.15
Here, once the units are in place, it's clear that the two sides
of the equation are dealing with different kinds of quantities:
d dimes + n nickels = 1.15 dollars Oops!
(d dimes * 0.10 dollars/dime)
+ (n nickels * 0.05 dollars/nickel) = 1.15 dollars Better