How come 7,271,000 mm^3 is equivalent to 7,271 cm^3 ?

[chriscarson]

Homework Statement

mm to cm

Relevant Equations

7271000mm3 or 7271cm3)

how come 7271000mm3 is equivalent to 7271cm3) ?

from mm to cm you should go back two zeros back right ?

 

[BvU]

No ! 10 mm = 1 cm

milli from mille, 1000
centi from centum, 100

 

[PeroK]

What is a $mm$? What is a $cm$? What is a $mm^3$? What is a $cm^3$?

 

[BvU]

From: https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf page 23:

 

[chriscarson]

No ! 10 mm = 1 cm

milli from mille, 1000
centi from centum, 100

I Didin t realize that

 

[chriscarson]

What is a $mm$? What is a $cm$? What is a $mm^3$? What is a $cm^3$?

so if it was nt cubed I was right then ?

 

[PeroK]

so if it was nt cubed I was right then ?

I'm afraid not.

 

[chriscarson]

I'm afraid not.

ok so that s not the difference

 

[BvU]

1 cm³ = 1 cm * 1 cm * 1 cm = 10 mm * 10 mm * 10 mm

elementary school stuff in developed (metricated) countries

 

[chriscarson]

1 cm³ = 1 cm * 1 cm * 1 cm = 10 mm * 10 mm * 10 mm

elementary school stuff in developed (metricated) countries

so 1 cm3 is equal to 1000mm3

 

[BvU]

Bingo !

 

[chriscarson]

Bingo !

It s new to me till now i only made for example 5000 mm is 500 cm , that s why i said you go back just one zero back ,

 

[BvU]

Did you say that ? I read

from mm to cm you should go back two zeros back right ?

 

[chriscarson]

Did you say that ? I read

yeah i was wrong there

 

[BvU]

All clear now ?

 

[chriscarson]

yes thank you for your time .

 

[PeroK]

From: https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf page 23:View attachment 268578

To quote Steely Dan: the things that pass for knowldege I can't understand.

 

[chriscarson]

To quote Steely Dan: the things that pass for knowldege I can't understand.

oh a book for help , thanks again

 

[archaic]

I usually do them like this $7271000[mm]^3=7271000[10^{-1}cm]^3=7271000\times10^{-3}[cm]^3=7271[cm]^3$

 

[etotheipi]

There is a benefit for saying volumetric units like "cubic centimetres" instead of "centimetres cubed". The former is unambiguous: $$\text{cubic centimetres} = (\text{cm})^3 = (10^{-2}\text{m})^3 = 10^{-6}\text{m}^3$$whilst the latter could be interpreted in two different ways:$$(\text{centimetres}) \, \text{cubed} = (\text{cm})^{3} = (10^{-2}\text{m})^3 = 10^{-6}\text{m}^3$$ $$\text{centi} \, (\text{metres cubed}) = 10^{-2} (\text{m}^3) = 10^{-2} \text{m}^3$$The former is what is always meant whenever someone says "centimetres cubed", but the wording can be ambiguous. In other words, the English language is not associative

 

[jbriggs444]

There is a benefit for saying volumetric units like "cubic centimetres" instead of "centimetres cubed". The former is unambiguous: $$\text{cubic centimetres} = (\text{cm})^3 = (10^{-2}\text{m})^3 = 10^{-6}\text{m}^3$$whilst the latter could be interpreted in two different ways:$$(\text{centimetres}) \, \text{cubed} = (\text{cm})^{3} = (10^{-2}\text{m})^3 = 10^{-6}\text{m}^3$$ $$\text{centi} \, (\text{metres cubed}) = 10^{-2} (\text{m}^3) = 10^{-2} \text{m}^3$$The former is what is always meant whenever someone says "centimetres cubed", but the wording can be ambiguous. In other words, the English language is not associative

And here I thought you were going to head for ( 7271 centimeters ) cubed versus 7271 ( centimeters cubed ). The former evaluates to 3.84 x 10¹¹ cubic centimeters and is the preferred meaning. The later is, of course, 7271 cubic centimeters.

 

[etotheipi]

And here I thought you were going to head for ( 7271 centimeters ) cubed versus 7271 ( centimeters cubed ). The former evaluates to 3.84 x 10¹¹ cubic centimeters and is the preferred meaning. The later is, of course, 7271 cubic centimeters.

Yeah, there's that too! You have to worry about $x\,(\text{cm})^3$ vs $x\, \text{c}(\text{m}^3)$ vs $(x\, \text{cm})^3$! What a mess! So much better to just say $x$ cubic centimetres, $x\,(\text{cm})^3$.

 

[Lnewqban]

so 1 cm3 is equal to 1000mm3

In similar way, 1 $dm^3$ equals 1000 $cm^3$.
For that reason, liters ($dm^3$) are frequently used for quantifying the displacement of engines rather than cubic centimeters (c.c.).
Example: General Motors engine LS7 is a 7,011 c.c. (7.0 L; 427.8 cu in) engine.

 

[chriscarson]

Too complicated for me the rest of the comments but thank you all any way.