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

  • Thread starter nukeman
  • Start date
In summary, the conversation is about finding the volume of a room in m^3 instead of dm^3. The correct method involves converting dm to m and then cubing the result. The correct answer is 1.08x10^5 m^3.
  • #1
nukeman
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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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  • #2
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.
 
  • #3
Ohh..hmm, so is this how you do it?

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

= 1.08x10^5 ? m^3
 
  • #4
That works :smile:
 
  • #5


To convert from dm^3 to m^3, you need to divide by 1000, since there are 1000 dm^3 in 1 m^3. Therefore, the correct conversion would be:

1.08x10^8 dm^3 / 1000 = 1.08x10^5 m^3

Your mistake was in dividing by 0.1, which would only be correct if you were converting from cm^3 to m^3. Also, note that your proposed solution would result in a larger volume, which does not make sense since dm^3 is a smaller unit than m^3. Always make sure to check your units and use the correct conversion factor when converting between different units.
 

1. How do you convert 1.08 x 10^8 dm^3 to m?

To convert from dm^3 to m, you need to multiply the value by 0.001. Therefore, the conversion for 1.08 x 10^8 dm^3 to m is 1.08 x 10^5 m.

2. What is the significance of the exponent in the conversion problem?

The exponent, in this case, represents the power of 10 that is being used in scientific notation. It indicates the number of decimal places that the decimal point needs to be moved to the left or right.

3. Can you explain the difference between dm^3 and m?

dm^3 and m are both units of volume, but dm^3 is a larger unit than m. 1 dm^3 is equal to 1000 m^3. Therefore, when converting from dm^3 to m, the value will decrease.

4. How do you know whether to multiply or divide when converting units?

The direction of the conversion depends on the relationship between the two units. If the unit being converted to is larger, then you will divide. If the unit being converted to is smaller, then you will multiply. In this case, since m is smaller than dm^3, we need to multiply to convert from dm^3 to m.

5. Are there any other units that can be used to measure volume besides dm^3 and m?

Yes, there are many other units that can be used to measure volume, such as liters, gallons, and cubic inches. The choice of unit often depends on the context or the specific scientific field being studied.

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