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## Algebra 1

### Course: Algebra 1 > Unit 3

Lesson 2: Appropriate units# Formulas and units: Comparing rates

When using formulas to calculate real-world quantities, we need to make sure our units are consistent. In this video, one growth rate is given in centimeters per week and the other is given in millimeters per day. In order to compare which rate is faster, we need to convert one of the rates to units that match the other rate.

## Want to join the conversation?

- ok is everybody watching a different video or am i missing something? because all see him talking about is the plant growth.(16 votes)
- He is actually talking about how to convert between units. The plant growth is just an example(2 votes)

- So in this case, Y stands for yield, C stands for carrots, and P stands for plants?(6 votes)
- my plant grows less then a millimeter per week.. (i measured it)(7 votes)
- Yes most plants grow slowly(1 vote)

- why the answer is
`C/P`

if we have`2C/P`

, but the answer is`C^2/P`

if we have`C^2/P`

?

I mean we are multiplying the number in situations, why do we write what are we multiplying by when we multiply buy the number/variable itself, but not when we multiply by other number ?(3 votes)- 2c/p say the C is 8, you have 16 carrots per plant which is c/p No lets say you have c^2/p for plants and still say C is 8. this comes out to be 64 Carrots per plant which is still c/p.(3 votes)

- I'm still incomprehension this question

Who can help me?(3 votes)- Hi,

So basically, Sal gives the growing speeds of plants that are possessed by two different people. He wants to know which grows faster, which we can do by converting both to the same units

- Fellow Khan Academy User(1 vote)

- At2:13, does Sal mean that the overall yield is 2/3 carrots or 2/3 carrots per plant?(2 votes)
- I think he means that the overall yield is 2/3 carrots per plant. I could be wrong though... It does sound wierd.. 2/3 Carrots per plant? that means you will never get a full carrot!(1 vote)

- I understand Sal solving this formula mathematically, but I don't really get the words of the question, and I don't understand what all these carrot yields, the expected carrots, or the plants are. I know it is about numbers of carrots produced, but I still can't understand how all these variables effect and how it all works. Please someone explain to me how all this "carrot harvesting" works with "carrot yields", the "expected carrots", or the "plants"(2 votes)
- Well I think it's just a formula that a person created based on his carrot yield. it's just a formula and it is not always true. If you wanted to create a formula for every carrot farmer, you would have to take in all the different variables. So to sum it up, it's just an assumption formula.(1 vote)

- I converted martine's millimetres into a proportion of cm which is 3/10 cm and martine's 1 days for each 3mm as a proportion of 1 week being 7 days as 1/7 weeks. So 3/10 cm=1/7Week-So 3/10=1/7-So multiply both sides by 7 to give 1 week (1/1w) and the other side multiplying 3/10 times 7 giving 21/10 giving 2.1 cm per 1 week(2 votes)
- Yes, that works as well.(1 vote)

- Ok, just to make things clear for me: the measurement unit for "Carrot yield" is actually more or less a measurement for a good or bad harvest? Like, if we had much more plants than how much carrots have grown, there was a bad harvest(2 votes)
- pretty much... although i dont know that that was the point😉(1 vote)

- In the formulas and units practice there’s an exercise where the answer is to convert the cubic cm to liters. Shouldn’t it be centiliters? And they don’t even cube the liters. I don’t get it.(1 vote)
- Centimeters is a linear measurement (used to measure distance).

Centimeters^2 is used to measure area (2-dimensional space)

Centimeters ^3 is used to measure volume (3-dimensional space).

Some units are defined to measure volume. Liters, gallons, etc. are examples. So, no exponent is needed on these.

Whenever you need to convert between units of measure, find the conversion ratio.

1 cm^3 = 1 milliliter = 0.001 liters.

Or, it takes 1000 cm^3 to make 1 liter.

So to convert from cm^3 to liters, just divide by 1000.

Hope this helps.(2 votes)

## Video transcript

- [Instructor] We're told
that Hannah and Martine each got a plant for their home. Hannah measured that her plant grows, on average, 2 centimeters per week. Martine measured that her plant grows, on average, 3 millimeters per day. Which plant grows faster? Pause this video and see if you can figure that out on your own. All right, now let's go
through this together. So at first when you look at it, you might just compare 3 to 2 and say, oh, 3 is larger than 2, therefore maybe Martine's
plant grows faster. And you would think that
until you look at the units. This is millimeters per day while for Hannah's plant it's in centimeters per week. So in order to really compare them we have to convert them to the same units in both length and time. So let's convert both of them, let's convert them both
to centimeters per week. You could just try to convert both of them to millimeters per day or I guess you could try
to convert both of them to meters per year, a third set of units, but centimeters per week seems reasonable since we already have
Hannah's plant rate at, so let me write this down. So Hannah, I'll just write H, grows at 2 centimeters per week. And then you have Martine, grows at an average of
3 millimeters per day. Now how do we convert
3 millimeters per day to centimeters per week? Well, first we could
convert the millimeters, actually, first, let's
convert the days into weeks. So how many days are there in a week? Well, there's 7 days in a week. So if we have how many
millimeters per day, if we wanted to know millimeters per week we would multiply times 7 days. So let me do that. So times 7 days in a week. That would get us, this would be equal to 3 times 7 which is equal to 21 millimeters in a week. And you can see, actually, that the units cancel
out nicely like that, so you're left with millimeters a week. And that makes sense, 3 millimeters a day, you're able to do 7 times that in a week, 21 millimeters a week. And then when you think
about 21 millimeters is how many centimeters? Well, we just have to remember that 1 centimeter is
equal to 10 millimeters, so if we wanna covert
this into centimeters, we essentially have to divide by 10. We could just say 1/10 of
a centimeter per millimeter and then that gets us, we could write it in different ways, but we could write this, and even here the units cancel out nicely, 21 divided by 10 is 2.1
centimeters per week. Another way you could
have just thought about it is we could say 1 centimeter
is equal to 10 millimeters, or if you divide both sides by 10, 1/10 of a centimeter is
equal to 1 millimeter, and if 1 millimeter is equal
to 1/10 of a centimeter then 21 millimeters is just
going to be 21 times this, 21 times 1/10 is the same
thing as 21 divided by 10, it would be 2.1 centimeters. And so now we can compare
2.1 centimeters per week compared to 2 centimeters a week. Well, it turns out that when you actually compare
the appropriate units it still turns out that Martine's plant is growing just a little bit faster.