Unit Conversions

www.alexandertutoring.com Sean here with Alexander Mathematics and Physics Tutoring, welcome to a new semester! As you know I like to save you time and effort by covering what I think are the most important lessons in math and physics. Today I want to talk about unit conversions, especially for my my students going in their first year of high school. This is something you will use in all of your science classes throughout your high school career. Let's say we want to change 10 meters to centimeters. The most common mistake that I see students make is to multiply when they should divide or divide when they should multiply. The procedure I’m going to give you will prevent this mistake every time. The first thing to do is write down the unit you are starting with, in this case 10 meters. Then we draw a set of open and closed parentheses with a division line through the middle. We want the meters to cancel out so we put meters on the bottom of the dividing line. We want to end up with centimeters, so we put cm on the numerator. It’s these units that tell you where to put the numbers. There are 100 centimeters in 1 meter, so we put 100 in the numerator and 1 in the denominator. We are now multiplying fractions, so we multiply across the top and bottom to get 1000 over 1, or 1000 centimeters. Now let’s do it in the opposite direction, changing 10 centimeters to meters. We will follow the exact same procedure. First we write down 10 centimeters, then draw our parenthesis with the division line. We want the centimeters to cancel out so we put them in the denominator. We would like to end up with meters so we put them in the numerator. Again there are 100 centimeters in a meter so we put 100 in the denominator and 1 in the numerator. Multiplying fractions across the top and bottom we get 10 divided by 100 or .1 meters. See how the units do all the hard work for you? Finally we need to look at the case of square units or cubic units, representing area and volume respectively. In this case the procedure is the same except we square the parentheses in the case of area, and cube them in the case of volume. So let’s say we want to change 10 square meters to square centimeters. We start off by writing 10 meters squared, put in our parentheses and division line, then square the parenthesis. We want the meters to cancel so we put them in the denominator, and centimeters in the numerator. The square on the parenthesis acts on both units to make them square units. We put 100 in the denominator and 1 in the numerator. Now recall that when you square a fraction you square both the numerator and denominator, giving us 10,000 up top and 1 down below. Multiplying across the top and bottom we get 100,000 square centimeters. That’s a lot! But if you think about it 10 square meters is a square that is 10 meters long and 10 meters high. A square centimeter is tiny, so imagine how many of them it would take to cover up the 10 square meters. Ok I hope this helps. I wish you all a wonderful remote semester, good luck!