Converting Units

What if you went to the grocery store and bought 3 gallons of milk? Could you determine how many pints of milk you purchased? Or how about if you bought 16 pints of milk? How many gallons would this be? In this Concept, you'll learn to make conversions like these so that you can solve real-world problems.

Real-world information is given in dimensions, or the units in which the value is measured. For example, the following are all examples of dimensions.

• Inches
• Feet
• Liters
• Micrograms
• Acres
• Hours
• Pounds
• Students

Analyzing dimensions can help you solve problems in travel, astronomy, physics, engineering, forensics, and quality. 


Example 1: lets imagine you have been training for a running race and you know you can run 3 miles. Your friend wants you to sign up for a 5km race. Can you run that distance? First you have to convert km to miles so you can compare the distance of the race to the distance you know you can currently run. 

You know that 1 mile = 1.609 kilometers. But how can you use this to convert the race distance to miles? Here is one way you can set up the problem.

1. Start with the unit you want to convert. In this case it is 5km. Draw a line under the unit and then a line to the side like this:

2. Then add the conversion factor. You know that there are 1.609km in every mile so put 1.609km on the bottom and 1 mile on the top. 

3. This will allow you to cancel out the km units. This works because when you divide anything by itself you get 1.

4. You can now solve the problem. Start by multiplying the numbers on top of the line. 
5x1 = 5.  
Then divide by the bottom number. 
5/1.609 = 3.107.

Example 2: Lets try another one. Usain Bolt ran 200 meters in 19.19 seconds. But how many miles per hour is that speed? (miles per hours is abbreviated MPH). We are going to use the same method as above. There are just a few more steps. 

1. Start with the units you want to convert. In this case it is 200meters/19.19 sec. In this case there is already a line between the units. 

2. Then add the conversion factor. We are going to worry about one unit at a time. Lets start with converting to miles. You probably don't know how many meters there are in a mile. But you do know You might know that there are there are 1000m in every 1km.

3. But we still have to get the equation into meters. Well if you remember from the question above we know that there are 1.609km in every 1 mile. So now our equation looks like this. 

4. Remember: when arranging the conversions you always need the units to cancel out. So if the meters is on the top at the beginning then in the next step the meters have to go on the bottom. You can now cross out the units that cancel out.

5. But we aren't done yet. We still need to convert from seconds to hours. We can add this directly to the equation we already have. We know that there are 60 seconds in 1 min (thats the first conversion to add) and we know that there are 60 minutes in 1 hour (thats the second conversion to add). 

Then ...

6. We can now cross out all the units that cancel out. In the end we are left with just the MILES and just the HOURS. Which is exactly what we wanted to convert into. 

7. Now it is time to multiply the numbers on top together and multiply the numbers on the bottom together. 

8. If we simplify this we will get:

9. And if we simplify it one more step we get:

So if you see Usain Bolt running on the road by the school he would actually be SPEEDING as he would be traveling at 23.32 MPH while the speed limit in a school zone is 20 MPH.

Below is a video to watch that will hopefully make this easier. The second video is for solving harder conversions in which you have to convert more than one unit (like the second example above).