 To convert between units, remember you can multiply by 1 without changing a value. 1 is a fraction where numerator and denominator are equal, and units act like algebraic variables. Let's convert 18 feet into meters, and we'll use the fact that 1 mile is 5,280 feet, and 1,000 meters is 0.625 miles. So we have 18 feet, and we want to have 18 feet, and we can maintain equality by multiplying by 1. Now, since 1 mile is 5,200 80 feet, then 1 is any amount divided by itself. So 5,200 80 feet is the same as 1 mile. So one form of 1 is 5,280 feet divided by 1 mile, or we could also use the reciprocal. And here's the important thing. We choose the form of 1 we can use to eliminate feet. So that means we want feet in the denominator, so we can then remove a common factor. Now, we'll worry about the computation later. The first thing to note here is the feet can be removed as a common factor, and so now our units are miles, which is not what we want. So we look to our other conversion factor, and we know that 1,000 meters is 0.625 miles. So again, 1 is any quantity divided by it's equal. So 1,000 meters and 0.625 miles are the same. So 1 is or again, we can use the reciprocal. And again, we want to choose the form of 1 that we can use that eliminates miles. And so that would be the form where miles is in the denominator. So we'll remove our common factors, and we see that the units left are meters, which is what we want. To compute the value, let's ignore the units for a moment and treat this as a purely numerical problem. In that case, we'd multiply the numerators and the constant, multiply the denominators, and evaluate the fraction. Now put things back where we found them. We did have units. And our final answer will be in meters. Nothing important changes if we have a derived unit like area. So we want to convert into square meters 0.035 square kilometers. So we have 0.035 square kilometers, and we still want to have 0.035 square kilometers. We have 1,000 meters equal to 1 kilometer, so we can multiply it by either 1,000 meters divided by 1 kilometer or 1 kilometer divided by 1,000 meters. Since we want to get rid of the kilometers, we'll choose the form that has kilometers in the denominator. And so we multiply. We'll ignore the units momentarily to get the numerical value 35. But what about the units? Units act like algebraic variables. So the kilometer in the denominator can remove one factor of the kilometer in the numerator that does leave one factor of kilometers. And we've introduced another unit of meters. So this numerical value 35 has units of kilometer meters. Well, that's not quite what we want, but we can get rid of that other factor of kilometers by, again, multiplying by 1, which is to say 1,000 meters divided by 1 kilometer. We compute and our units will be meters squared, which is what we want. Or let's convert 12 feet per hour into a speed in inches per minute. So 12 feet per hour is the same as 12 feet per hour, and we know that 12 inches equals 1 foot. So 1 is 12 inches divided by 1 foot or 1 foot divided by 12 inches. Since we want to eliminate feet, we'll choose the form that eliminates a factor of feet, which will be. And we also want to eliminate hours. So we know that one hour is 60 minutes, which gives us a couple of forms of one. And again, this time we'll want to choose the factor that eliminates the hour, which is in the denominator. We'll ignore the units for a moment to compute our numerical value and then simplify our units to get the units of our answer, which are what we want them to be.