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# Why is the power on the end of units negative? Watch

1. I commonly see units written with a negative power e.g. 5kg/m-3. If it is metres cubed, why is it negative? A negative power would turn it into a fraction?
2. (Original post by pelaitsc45)
I commonly see units written with a negative power e.g. 5kg/m-3. If it is metres cubed, why is it negative? A negative power would turn it into a fraction?
We write 5kgm^-3 that is the same as 5kg/m^3.

The negative power shows is 'per' ie velocity is 5ms^-1 or 5 metres per second.
3. (Original post by pelaitsc45)
I commonly see units written with a negative power e.g. 5kg/m-3. If it is metres cubed, why is it negative? A negative power would turn it into a fraction?
Do you mean you see 5kgm^-3? Because 5kg/m^-3 is just 5kgm^3.

You're correct that the negative power makes it a fraction in a sense. Think about what the units are describing. In this case it's density, and you're saying that the density is five kilograms, for every cubic metre of volume.

To arrive at this density you will have divided the overall mass (measured in kg) by the volume (measured in cubic metres), and therefor you have units that are kilograms per/divided by cubic metres. This can be expressed as kg/m^3 or kgm^-3.

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4. At AS and above, we start writing units in this way. If you think of velocity as distance over time, you can see where the unit m/s has come from: distance in m divided by time in s to give m/s.

If you take maths, you'll know that 1/s is the same as s^-1 (to the power of -1). Multiplying 1/s by m gives you m/s which is thus equivalent to ms^-1.

When writing in this format, make sure not to include the /. e.g. 5kg/m^3 becomes 5kmg^-3, and 3m/s^2 becomes 3ms^-2.
5. (Original post by Ed5)
At AS and above, we start writing units in this way. If you think of velocity as distance over time, you can see where the unit m/s has come from: distance in m divided by time in s to give m/s.

If you take maths, you'll know that 1/s is the same as s^-1 (to the power of -1). Multiplying 1/s by m gives you m/s which is thus equivalent to ms^-1.

When writing in this format, make sure not to include the /. e.g. 5kg/m^3 becomes 5kmg^-3, and 3m/s^2 becomes 3ms^-2.
Oh okay, that clears things up massively. Thanks.

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Updated: September 13, 2016
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