Conversions

[mike2345]

Hello, this is my first time posting:-)

 

I have a question about conversion. I'm doing grade 8 science and in my book it says that the unit of "cc" is the same as "mL". This is all the info they give me. Then I'm asked to convert this value: 100 microL to cc? I have no idea how to do this so I looked in the answer key and the answer is: 0.1mL=0.1cc. Would someone be willing to explain the how and why? It would be greatly appreciated!!!

[DJBruce]

The definition of a litre is one cubic decimeter. A cubic decimeter is a cube that is 10 cm by 10 cm by 10 cm, so there are 100 cubic centimeters in a litre. Thus:

 

[math] 1000 cm^3 = 1 L = 1000 mL [/math]

 

[math] 1 cm^3 = .001 L = 1 mL [/math]

 

Knowing this the conversion you should realize that any measurement in mL is the same in cubic centimeters.

[mike2345]

Hey DJBruce, thank you very much for replying. I'm sorry but I'm still confused:confused: If possible, would you mind explaining it to me in a different way????

[darkenlighten]

Pretty much as he stated. 1 cubic centimeter is equal to 1 milliliter

 

Think of it this way: if you were to imagine a cube in which each side was a 1cm by 1cm square, so the volume of that square is (height X width X depth) = (1cm X 1cm X 1cm), which is the same as 1cm^3 or 1 cubic centimeter.

 

Now that you have this cube that has a volume of 1 cubic centimeter. Imagine filling this cube with water. How much water that is in this cube is 1 mL; therefore 1 cm^3 = 1 mL

[mike2345]

Hello darkenlighten, thanks for replying.

Okay so I understand part of it. ml=cc. So 20kL is 20,000,000cc. What I'm having trouble with is why 1 liter is equal to 1 cubic decimeter and why 1ml is equal to 1 cubic centimeter? Does it work this way all the way across the metric number line?? Again I'm sorry for so many questions.

[DJBruce]

A litre is defined as a cubic decimeter. This is because at the 1964 Conférence générale des poids et mesures, GCPM, the agreed to define the litre as an alternative definition for a cubic decimeter. A cubic decimeter is 10cm long, 10cm wide, and 10cm high. To find the volume of such a container we do length times width times hieght.

 

[math] v=lwh [/math]

[math] v=(10cm)(10cm)(10cm)=1000 cm^3 [/math]

 

So a litre is defined as 1000 cubic centimeters. In a litre there are 1000 mL, as the prefix milli means one one-thousandth. So the reason that a milliliter equals a cubic centimeter is because of the definition of litre and the definition of the SI prefix milli.

 

I hope this makes sense.

[Sisyphus]

The square of a distance is an area, and the cube of a distance is a volume. Liters are also a measure of volume. So cubic meters and liters are measures of the same thing: volume. So you can convert directly between them in a fixed ratio. The metric system is set up so that one milliliter is exactly equal to one cubic centimeter.

 

And yes, units in the metric system relate to one another in simple ways like that, on purpose. You'll see this a lot more when you study more science, especially physics.

[mike2345]

Thanks for the replies.

 

Okay so then how would you convert 1kiloliter to cubic decameters?

And 1 decaliter to cubic decimeters?

[Sisyphus]

Thanks for the replies.

 

Okay so then how would you convert 1kiloliter to cubic decameters?

And 1 decaliter to cubic decimeters?

 

What would you guess, and why?

[mike2345]

Okay so, there is 100 decaliters in 1 kiloliter so to change decaliters to decameters: 100dam x 100dam x 100dam = 1,000,000dam^3

 

For 1 decaliter to cubic decimeters: There is 100 deciliters in 1 decaliter so to change decaliters into decimeters: 100dm x 100dm x 100dm =

1,000,000dm^3.

[DJBruce]

Try converting decameters to litres then ember the definition of a litre. This should make this problem easier.

 

To do the conversion this way all you need to know is how many litres are in a decaliter, and what a litre is defined is. To find the definition of litre is one of my posts above.

[Sisyphus]

Ok, a few things:

 

You wouldn't change decaliters to decameters, since they're measures of different things: volume and length. A cubic decameter is a measure of volume.

 

One thing I always suggest is the "does this answer make sense" test. Imagine a cubic decameter: a cube 10 meters (about 39 feet) on a side. In other words, a really big cube. Your answer says that 1 million of those is the same as 1 kiloliter, or just 1000 1 liter bottles. Obviously that's way too many.

 

I'm not sure why you're multiplying 100^3, so I'll just say how I would do it, and you can figure out where you went wrong yourself.

 

Now, what you know is that 1 milliliter is equal to 1 cubic centimeter, right? So how many milliliters in a kiloliter? 1000 milliliters per liter X 1000 liters per kiloliter = 1 million milliliters per kiloliter.

 

Next, how many cubic centimeters per cubic decameter? How many little tiny cubes fit inside the one giant one? Well, there are 100*10=1000 centimeters in a decameter, right? But that's not the same as cubic centimeters. 1000 cubic centimeters all in a line would just be one edge of the giant cube. The giant cube is 1000 little cubes wide, 1000 little cubes high, and 1000 little cubes deep. So the whole thing is 1000*1000*1000=1,000,000,000 (1 billion) cubic centimeters. Which means there are also 1 billion milliters in the giant cube, because that's the same thing.

 

So if there are 1,000,000 milliters per kiloliter, and 1,000,000,000 milliliters per cubic decameter, how many kiloliters per cubic decameter?

[mike2345]

I can't thank everyone enough, how much you guys have tried to help me but I'm still not understanding. Even after Sisyphus's very detailed explanation. I think you have to know when to throw in the towel. So thank you again.

[DJBruce]

If you are still confused you may want to approach your teacher about it. They might be able to help you understand it, and or demonstrate these ideas to you.

 

Sorry I could not of of more use.

[mike2345]

No need to apologize DJBruce.

 

Well I'm actually doing distance education so all my interactions with my teacher is through emails. My school is located in a town about an hour and a half away and I can't get out there. I honestly don't know why I am having such a problem with this. I've always excelled in science and math but this conversion I just can't seem to wrap my brain around. I keep trying to picture these conversions done on the metric number line and it doesn't work for me.

[hermanntrude]

OK here goes:

 

the conversion factor on a simple metric conversion:

 

convert 2.34 mm to m:

 

The conversion factor between mm and m is 1000. There are 1000 mm in a m. We can represent that as an equation:

 

1000mm = 1m

 

Or we could represent it as a fraction (conversion factor):

 

[math]\frac{1000mm}{1m}[/math]

 

The conversion factor is useful because technically it's equal to 1, so we can multiply any number by it and not change its overall value. We can also turn it upside down and not change its value. So we can multiply our 2.34 mm by our conversion factor and the only thing that will change is the units. the actual value won't have changed, although the number and the unit will.

 

2.34mm x[math]\frac{1m}{1000mm}[/math] = 0.00234m

 

Notice we had to decide which way up we wanted the conversion factor. the rule for that is "wanted over given" in this case meters over mm.

 

What about converting volumes? It's a bit more confusiong here but let me show you how it goes:

 

convert 1L (1dm^3) to m^3:

 

Now we can use the conversion factor again but we have to be careful either we can use the conversion factor for dm^3 to m^3 if we absolutely sure we know what it is, OR we can go back to basics and use the conversion factor between dm and m. if we do that, though, we must be sure to cube that conversion factor:

 

[math]1dm^3 \times (\frac{1m}{10dm})^3=1dm \times \frac{1m^3}{1000dm^3} = 0.001m^3[/math]

 

To apply this to your original question, the slight problem is that the units are difficult, and not easy to bring back to their original definitions in terms of simple distances, but remember that these are volumes, and the metric prefixes are already applied, so we don't need to get too deep into conversion factors this time. All you need to do is realise that the conversion factor between microliters and milliliters is 1000microliters = 1 milliliter. Then 100 micoliters becomes 0.1 ml, and you're given the information for cc to ml:

 

[math]100\mu L \times \frac{1mL}{1000\mu L} \times \frac{1cc}{1mL} = 0.1cc[/math]

 

Ideally, you'd cancel out the units as you wrote this but I haven't found a way of showing that. Notice that all the units you don't want appear both above a line and below one, so they cancel out, and you're left with a unit you DO want. The math looks awfully long and drawn out but it's actually what you ought to be doing every time you do a conversion from one unit to another, even when the conversion factor is 1 to 1 (like cc and mL).