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 like it's common for students to jump in with an equation likeI 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 |