About a volume conversion..?

[1123581321]

Hi,

 

Ive recently worked on a chemistry question which required a volume conversion from cm^3 to m^3

 

Specifically the number was 10 cm^3 and it shouldn't have been as difficult as its ended up being, but i eventually got the right answer.

 

However, the method which gave the right number, was in the format of: (10 cm^3 / 1) * (...m^3 / ...cm^3) = 0.00001, of which turned out from

(10 cm^3 / 1) * (0.001 m^3 / 1000cm^3), which seems to give the right conversion factor.

 

This was worked out from equating them as follows: 10 cm^3 = 0.1 m^3 ... then, (10)^3 cm^3 = (0.1)^3 m^3 ... which gives 1000 cm^3 = 0.001 m^3, and then using those values in the equation (the process stated).

 

The problem however is that while this works, it doesn't seem to work out the same via the process of simply going:

(10 cm * 10 cm * 10 cm) / (100 cm * 100 cm * 100 cm) = ..

 

And since its a volume (or in cubic units), why exactly should accounting for the volume by means of, (x * y * z) / (x * y * z) to put it that way, not work the same ???

 

Thanks.

Edited November 13, 2013 by 1123581321

[John]

This was worked out from equating them as follows: 10 cm^3 = 0.1 m^3 ... then, (10)^3 cm^3 = (0.1)^3 m^3 ... which gives 1000 cm^3 = 0.001 m^3, and then using those values in the equation (the process stated).

A minor nitpick here: The first equation should be 10 cm = 0.1 m. The rest of your reasoning then follows.

 

The problem however is that while this works, it doesn't seem to work out the same via the process of simply going:

(10 cm * 10 cm * 10 cm) / (100 cm * 100 cm * 100 cm) = ..

 

And since its a volume (or in cubic units), why exactly should accounting for the volume by means of, (x * y * z) / (x * y * z) to put it that way, not work the same ???

You have cm³ in both the numerator and denominator, and so they will cancel out. However, what you will end up with is (10 cm)³ / (100 cm)³ = 0.001, which makes sense since 100³ cm³ = 1000000 cm³ = 1 m³. This is why unit conversion involves multiplying ratios of different units together to arrive at a final sensible unit for the result. In this case, to match your previous reasoning in expressing (10 cm)³ = 1000 cm³ as some number of m³, you'd want:

 

[math](10 \textnormal{cm})^{3} \times \frac{(1 \textnormal{m})^{3}}{(100 \textnormal{cm})^{3}} = 1000\textnormal{cm}^{3} \times \frac{1 \textnormal{m}^3}{1000000 \textnormal{cm}^{3}} = \frac{1000 \textnormal{cm}^{3}}{1000000 \textnormal{cm}^{3}} \times 1 \textnormal{m}^{3} = 0.001 \textnormal{m}^3[/math]

Edited November 13, 2013 by John

[1123581321]

Thanks for the explanation John. Thats the answer i came across as well, however i checked it again by plugging the numbers into a unit conversion website and it seemed to give back 0.00001 which I'm still confused about but it seems to work out in the question I'm doing. So I'm still on the sidelines a bit with it. Any reason u can think of why it would have given that number..?

[John]

Well, 10 cm³ is indeed 0.00001 m³. Note that 0.00001 is one hundred-thousandth. Since we've shown that 1 cm³ is one millionth of 1 m³, it follows that 10 cm³ must be one hundred-thousandth of 1 m³.

 

Without knowing what exactly you plugged in, I don't know what problem you're encountering (if any) or how to solve it.

[mathematic]

(10 cm * 10 cm * 10 cm) / (100 cm * 100 cm * 100 cm) = ..

 

10cm^3 is NOT (10cm)^3.

[1123581321]

Hi John,

 

Yes that does make sense, however i guess my question is more so why exactly simply going: 10 cm^3 = 0.1 m^3 ... then (10)^3 cm^3 = (0.1)^3 m^3 ... then 1000 cm^3 = 0.001 m^3, doesn't give you the right answer, whereas going through the process of finding a conversion factor and then multiplying it by the given value works ?

 

Thanks.

[John]

1000 cm³ = 0.001 m³ is correct. If you have that equation and wish to know the conversion factor for 10 cm³, then you'll want to divide both sides of the equation by 100, i.e. 1000 cm³ / 100 = 0.001 m³ / 100, which will give you 10 cm³ = 0.00001 m³, as desired.

Edited November 14, 2013 by John

[mathematic]

Hi John,

 

Yes that does make sense, however i guess my question is more so why exactly simply going: 10 cm^3 = 0.1 m^3 ... then (10)^3 cm^3 = (0.1)^3 m^3 ... then 1000 cm^3 = 0.001 m^3, doesn't give you the right answer, whereas going through the process of finding a conversion factor and then multiplying it by the given value works ?

 

Thanks.

"10 cm^3 = 0.1 m^3" is wrong.

[Ehab]

This short video will help you understand the concept