How to convert 125 cm^3 to m^3?

- Fanduekisses

How to convert 125 cm^3 to m^3?

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- Fanduekisses

\[125 cm^3 \rightarrow m^3\]

- Fanduekisses

like conversion

- DanJS

start with what you are given, and multiply that by ratios of 1, until you get the units you need

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## More answers

- Fanduekisses

times 10^-2?

- Fanduekisses

1cm is 1m x 10^-2 right?

- DanJS

|dw:1443321639394:dw|

- DanJS

just do the normal relationship between cm and m, then cube both

- DanJS

10^(-2) m = 1 cm
cube both sides
10^(-6) m^3 = 1 cm^3

- Fanduekisses

so 125 x 10^-6 m^3 ?

- DanJS

|dw:1443321895711:dw|

- DanJS

the cm^3 unit cancels from numeratior and denominator, so you cant mix up multiplying or dividing by the 10^-6, otherwise the units wont work

- DanJS

That is the general way to do any sort of unit conversion, and other things
forget about the numbers till the very end, just start with the given, multiply by fractions of 1 so that the units cancel and move towards what you need, may take many more fractions than just 1 used here to change it over ...
good luck

- Fanduekisses

so it's 125 x 10^-6 m^3 ?

- Fanduekisses

thanks. :)

- DanJS

long as the units cancel out to leave the right one, the numbers should work themselves out, if you put each ratio value in right

- Fanduekisses

|dw:1443322494095:dw|
Oh ok what about 7.8 x 10^3 g/L to kg/mL?
I tried it

- Fanduekisses

|dw:1443322675739:dw|

- Fanduekisses

do the "10^3" cancel out even if they aren't in the same unit?

- Fanduekisses

Answer key says it's 7.8 x 10^-3 kg/ml

- Fanduekisses

oh and the answer key for the first one says it's 125 x 10^-3 m^3 not 125 x 10^6 m^3, why?

- DanJS

yeah , that simple, i always just remember how each unit relates to the base unit, then you just have to remember one thing only, like for a mL
1 mL is 10^-3 L
i always change the base unit to the other ones, easier to remember i think , maybe not

- DanJS

after you get the units right, all you have to do is multiply through all the top numbers, then divide through by all the bottom numbers to get the value

- DanJS

|dw:1443322956160:dw|

- DanJS

combine all the powers of 10, it simplifies down to 10^(-3)

- DanJS

oh yeah just saw what you typed above, yeah you can take care of all the constant numbers all at once , the unit it came from doesnt matter, just think of the unit as another term in the thing tha tis being multiplied to it's number,
the thing is just a bunch of multiplication and division, you can do that in any order

- Fanduekisses

ohhhh I see know.

- Fanduekisses

Thank you! ^_^

- DanJS

yep, no prob

- Fanduekisses

|dw:1443324302561:dw|
I still have a question: I got 125 x 10^-6 m^3 but in my text it says I should get 125 x 10^-3 m^3 ?

- Fanduekisses

m^3 *

- DanJS

hmm...

- DanJS

think the book typed it wrong

- DanJS

if you think about mini cubes with sides 1 cm
and
a huge cube with side 1 m
you will calculate that it will take 1 million small cubes to fill the large

- DanJS

Volume of both cubes at the time the small cm cubes fill the large m side length cube,
1m*1m*1m = 1 m^3
100 cm * 100 cm * 100 cm = 1000000 cm^3
a million cubic cm to fill a cubic meter or 1*10^6

- Fanduekisses

Yeah it must be wrong, well it's not an actual textbook, it's a handout my teacher gave us. Like it must be a typo or something.

- DanJS

Did the same thing in the problem, except forget rememboring higher dimension relationships like cm^3 to another length ^3
Relate them in the 1 dimensional way, then cube everything

- DanJS

[1 cm] = [10^(-2) m] all you have to remember, or have a prefix chart
1^3*cm^3 = 10^(-2*3) m^3

- Fanduekisses

Yeah I just looked at them and studied them. :) mili-10^-3, kilo-10^3, etc, etc. so useful! :D

- DanJS

If you are converting from some units like femptometer to Gigameter,
take the given femptometer and convert to the base unit meter first, then convert from meter to Gigameter

- DanJS

i always do even for ones you can manually think how many powers apart they are

- Fanduekisses

yeah.

- DanJS

you good for now at least...?

- DanJS

i have a sheet somewhere of like 150 ratios of 1 separated into sorta subjects.
mostly the English to SI factors

- DanJS

just kept keeping track

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