• If an object has a mass of 50g and takes up a space of 500ml, what is the objects density? By substituting the numbers into the equation, we will have:

• What if we are given an object's density and its mass and are asked to find its volume? Using what we have learned in algebra, we can convert the equation to find the answer. </STRONG>Whenever you see a * or x in an equation, it means to multiply.

Many times in science you will need to convert one unit of measurement to another. For example, you might be given a problem in kilometers, but need the answer in centimeters. The process of converting one unit to another is called dimensional analysis.
Dimensional analysis involves determining three important facts:

1. In what unit your measurement is given
2. In what unit it should be expressed
3. What relationship between the units will allow you to make the conversion.The relationship between the units is called a conversion factor . A conversion factor expresses an exact relationship between the original unit and the desired unit. It is a fraction whose value is 1.

Although the numerator (top) of the fraction and the denominator (bottom) of the fraction are different, their actual values are the same. For example 60 minutes equals 1 hour and 1 liter equals 1000 milliliters.
Any number can be multiplied by 1 without changing its value. Multiplying a measurement by a conversion factor , then, does not change the value of the measurement. This means that you can convert the given unit to the desired unit by multiplying by an appropriate conversion factor. You must, however, choose the correct form of the conversion factor. The unit to be converted must cancel out and the desired unit remain . Thus, the denominator of the conversion factor must contain the same unit as the one given to enable them to be canceled. Similarly, the numerator must contain the unit to be in the answer. (Ok a little confused with the last paragragh)

The following example shows how a typical dimensional analysis problem is solved.
Sample Problem: Your friend runs 2500 meters while you run 3 kilometers. Using kilometers, which one of you has run a longer distance?

• Step 1: Determine the given unit and the desired unit.
  • given: meters
  • desired: kilometers
• Step 2: Find the relationship between the units and consider the possible conversion factors. 1000 meters = 1 kilometer
• Step 3: Choose the conversion factor whose denominator has the same unit as your given value. (dont get that part)
• Step 4: Write the original value next to the conversion factor with a multiplication sign between them. Cancel like terms.
• Step 5 : Multiply the resulting equation.

Your friend has run 2.5 kilometers and you have run 3 kilometers. You have run the longer distance!
Let's try converting 4500 grams to kilograms. When we set up our conversion factor, we must arrange it so that our grams unit will cancel out and leave only kg.

• Step 1: Identify what units you would like your answer in. kg
• Step 2: What are we given to start with? 1357 grams
• Step 3: Begin writing an equation leaving space for the conversion factor between the two numbers.
  • 1357g x ??????? = ______ k
• Step 4: Set up the conversion factor so the beginning units cancel out and we are left with the final units for the problem.
  • 1357g x (1 kg / 1000 g) = ________ kg
• Step 5: Finish the problem by multiplying and dividing.
  • 1357 x 1kg / 1000 = 1.357kg

Now, this equation can also be looked at in a couple of different ways. Let's say that you are given the Distance and the Speed and you are asked to find the Time. What would that equation look like?

Copy this question to your notes because you will see it on your midterm. Rex is testing out his new red 2001 Pontiac Trans Am Firehawk. He decides to hop on the freeway and gun it. What is his speed if he travels 881 m in 3 seconds?
Most of the time, the speed of an object is not always constant. For example, you are driving from a rural community and travel at a speed of 80 km/hr for the first hour. As you enter the city, you hit rush hour and have to reduce your speed to 10 km/hr for the next hour. Finally you get through the traffic and can travel at 50 km/hr for the third hour. If you divide the total distance by the total time, you will get the average speed . This will not tell you the speed at every point.

The average speed of the driver is 47 km/hr. 80 km + 10 km + 50 km / 3 hours = 47 km/hr