*Simple conversion probelm - Converting 1.08 x 10^8 dm^3 to m

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SUMMARY

The discussion focuses on converting a volume measurement from cubic decimeters (dm³) to cubic meters (m³). The initial calculation incorrectly resulted in 1.08x10^10 m³ due to a misunderstanding of the conversion factor. The correct conversion involves recognizing that 1 dm³ equals 0.1 m on each side, leading to the formula 1.08x10^8 dm³ multiplied by (0.1 m/1 dm)³, which accurately yields 1.08x10^5 m³.

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Homework Statement



Just doing a review, and I am doing something wrong. I know its very simple, but can someone tell me what I am doing wrong.

The volume of a room is 1.08x10^8 dm^3

What is the volume in m^3?



Homework Equations



I am going ?m^3 = 1.08x10^8 dm^3 = 1 dm^3/ .1m
(so the dm^3 cancels out, leaving just the m, but my answer is: 1.08x10^10
And the correct answer is 1.08x10^5 m^3

can someone explain to me again how to do this? Thanks!



The Attempt at a Solution

 
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One dm is how many meters?

So how many m3 is a dm3? Hint: dm3 is a cube that is one dm on each side.
 
Ohh..hmm, so is this how you do it?

1.08x10^8dm^3 ((.1m/1dm)^3)

= 1.08x10^5 ? m^3
 
That works :smile:
 

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