In physics we are dealing with measurements that means that very number we encounter has to stand for some kind of measurement. The measurements we are dealing are part of different groups, these groups are called dimensions. For instance if an iPod costs $350, the number $350 is part of the dimension we call price. There are a lot of different dimensions but we will only be using three of them. These three dimensions are MASS, LENGTH and TIME. One of the dimensions you might think of might be volume, but volume is a comp0osiute dimension made up of three length dimensions: length, width (which is also a length) and height (which is another length).
The price of an iPod might be $350 in the US but would be only 300 Euro anywhere in Europe. The iPod is not cheaper in Europe just because the number is smaller. The number by itself does not mean anything in physics, there has to be a UNIT attached to the number to give it a meaning. If you have watched any science show like CSI you will have noticed that the units they use are different from what you are used to, that is because they are using the Metric System of measurements. Everywhere in science and even in the US Army the metric system is used. The reason for that is that the conversion from unit to another within the metric system is very easy. I will give some examples towards the end. However, you are not used to the metric system since in the US the English or Imperial system is still used. If you have traveled abroad you will remember that is became second nature to convert the prices to Dollar amounts. In order for you to succeed in physics the metric system also has to become second nature. You should be bale to tell that the with of a table I measured in meters and that the table in front of the classroom is roughly 3 meters long. Or that a 2 liter (another metric measurement) has a mass of 2 kilograms. In your workbook you will find several examples that will help you in your initial conversions. It helps to know that a yard is roughly a meter or three feet.
The process of changing the unit of a quantity without changing the value of that quantity is called reduction. For instance in class we will also do some exact conversions from feet to meter or from miles per hour to meters per second. I will show you below how this is done.
Here is a simple way on how to convert units. The unit conversion factor will always be given. For instance: 1 m = 3.2 ft. You can see that meter is the larger unit or the higher denomination, because it takes 3.2 ft to make 1 m.
In order to go from the higher denomination to the lower on you have to multiply by the number required of the lower denomination to make the higher one.
Convert 3 miles into meters (1 mi = 1600m). 3mi × 1600 = 4800m
In order to go from the lower denomination to the higher on you have to divide by the number required of the lower denomination to make the higher one.
Convert 350 miles into miles (1mi = 1600m). 350m / 1600 = 0.22mi
Convert 4 meters into feet (1 ft = 0.31m). 4m / 0.31 = 12.9 ft
The second example is a little more complicated, because we said above that meter is the higher denomination. So it seems that we are changing from the higher to the lower denomination, from meter to feet. But since the conversion is given “backwards” - 1 ft = 0.31m – we are actually changing from the lower to the higher and need to divide, because it takes 0.31 of the meters to make one foot. Although this might seem artificial or constructed is especially important when changing currencies. The main currency (how much of the other it takes to make one) is always the one of the country that you are in. These rules cannot be applied blindly. Think before you start the math.
The exchange rate between the US $ and the Euro is 1 Euro = $1.34 . If you were to look up the exchange rate between the two currencies in a European Newspaper what would it read?
If 1 Euro = $1.34 then 1$ US = 0.75 Euro. Both exchange rates are sometime given because they are both equally valid.
All of the above is true when you are changing units within the metric system, for instance if you are changing from meter to centimeter. However, the conversion factor will not be given. You can find them in the table below. Since the metric system is based on the factor 10, all that has to be done is to slide the decimal point over to the right digit. This is easy when you try to convert 3 m into centimeters, but seems harder if the numbers are not as easy to grasp.
Convert 0.03 meters into centimeters. You need to know that 1 m = 100 cm. Therefore you are changing from the higher denomination (meter) to the lower one. 0.03 m × 100 = 3 cm.