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## Algebra 1

### Course: Algebra 1>Unit 3

Lesson 1: Rate conversion

# Intro to dimensional analysis

Sal shows how we can treat units of measurement algebraically, and use these tools in order to convert between different units of the same quantity. Created by Sal Khan.

## Want to join the conversation?

• Does anyone know a better way of explaining what he's talking about? I am having difficulties applying what he said in the videos to the practice problems he's giving me. •    There is nothing much to worry We know distance = Speed * Time
We know the units for each of them
Distance = metre
Speed = metre/second
Time = Second
Now Using the equation:
D = S * T
D(m) = S(m/s) * T(s)
The quantity in the bracket is their unit

Let's say I am going at 20 m/s speed in 20 seconds. What is the distance I have traveled?
>>
D(m) = 20 m/s * 20 s
20*20=> 400 (That seems so simple isn't it?)
The s in the denominator(speed) and s in the numerator(seconds) cancel out. You are left with the meter on RHS which is the same unit on LHS, this is the basis of DIMENSIONAL (Using Dimensions) ANALYSIS (I don't have to give the meaning do I?) or DA

Let's say I travel at 5m/s for 1 hour. What is the distance?
If you are pretty fast your mind will think of converting time to s
Conversion:
1 hour has 3600 seconds(Ok mind is steady)
1hr(given in question) * 3600 s/1hr (read as 3600seconds per hour, logically that is correct right?)
Now calc the numbers and the units of hours cancel out leaving 3600 seconds.
Multiply with speed
5 m / s * 3600 s The seconds Unit cancels.You are left with 18000m.
If you have understood till here then you can try using DA to find 18000m in km..

Let me know if it still confuses you.
Nolan :)
• I don't understand why m/s * s cancels out the two s's? Wouldn't m/s *s/1 = ms/s? I know this is a really dumb question, but I just need a clarification I guess • In the practice, many of the problems have the problems expressed in meters squared or cubed, but the video does not explain how to handle the numbers when converting from say, cm3 to m3 (sorry I don't know how to subscript!) Are there any videos doing this type of rate conversion? •  With square units, you would need to square the conversion factor. Similarly, with cubic units, you would need to cube the conversion factor.

Since 100 cm = 1 m, 10,000 cm^2 = 1 m^2 and 1,000,000 cm^3 = 1 m^3.

Have a blessed, wonderful day!
• At ,i don't understand how he does the hour/second formula. It always gets me and I don't understand how it works. Can anybody help please? • bro didn't explain anything in this one... • Why do these problems, as usual, have no correlation with the exercise? These problems are nothing like the exercises • Why does this say d= rate x time ... so if I take the birth rate in the US and multiply it by a time, I will get a distance? •  This is only applicable to distances. If you take the birth rate and multiply it by a time, you will get population, not distance. The equations technically look the same, but you're going to get a goofy answer if your distance unit is babies*time.
• So how does this relate to the exercise presented after this video? • There is nothing much to worry We know distance = Speed * Time
We know the units for each of them
Distance = metre
Speed = metre/second
Time = Second
Now Using the equation:
D = S * T
D(m) = S(m/s) * T(s)
The quantity in the bracket is their unit

Let's say I am going at 20 m/s speed in 20 seconds. What is the distance I have traveled?
>>
D(m) = 20 m/s * 20 s
20*20=> 400 (That seems so simple isn't it?)
The s in the denominator(speed) and s in the numerator(seconds) cancel out. You are left with the meter on RHS which is the same unit on LHS, this is the basis of DIMENSIONAL (Using Dimensions) ANALYSIS (I don't have to give the meaning do I?) or DA

Let's say I travel at 5m/s for 1 hour. What is the distance?
If you are pretty fast your mind will think of converting time to s
Conversion:
1 hour has 3600 seconds(Ok mind is steady)
1hr(given in question) * 3600 s/1hr (read as 3600seconds per hour, logically that is correct right?)
Now calc the numbers and the units of hours cancel out leaving 3600 seconds.
Multiply with speed
5 m / s * 3600 s The seconds Unit cancels.You are left with 18000m.
If you have understood till here then you can try using DA to find 18000m in km..

Let me know if it still confuses you.  • 