Units confusion in calculations

[PonderingMick]

Can someone please explain how kg x kg-2 (in superscript) can equal kg?

I hope it does or my calc is wrong! Anywhere I can revise this kind of thing?

Mick

 

[tiny-tim]

Welcome to PF!

Hi PonderingMick! Welcome to PF!

Same way that 10 x 10^-2 = 10^-1

Why does that bother you? ​

 

[Mark44]

Can someone please explain how kg x kg-2 (in superscript) can equal kg?

I hope it does or my calc is wrong! Anywhere I can revise this kind of thing?

Mick

Hi PonderingMick! Welcome to PF!

Same way that 10 x 10^-2 = 10^-1

Why does that bother you? ​

So the upshot is that kg x kg^-2 doesn't equal kg.

 

[HallsofIvy]

Can someone please explain how kg x kg-2 (in superscript) can equal kg?

I hope it does or my calc is wrong! Anywhere I can revise this kind of thing?

Mick

Then, I am afraid, you calc is wrong.
$$kg \times kg^{-2}= kg^{-1}$$
which is the same as
$$\frac{1}{kg}$$
not kg.

 

[gb7nash]

Can someone please explain how kg x kg-2 (in superscript) can equal kg?

I hope it does or my calc is wrong! Anywhere I can revise this kind of thing?

Mick

Do you mean $$\frac{kg}{(kg)^2}$$?

The answer would be:

$$\frac{1}{kg}$$, not $$kg$$

 

[PonderingMick]

OK, I must be wrong before I get that far.

I have:

m x (ms^-1)²
N m² kg^-2

So on the top I get:
m x m²s^-2

and on the bottom I get

m kg s^-2 m² kg^-2

all the m and the s cancel so i just get the kg left

 

[uart]

OK, I must be wrong before I get that far.

I have:

m x (ms^-1)²
N m² kg^-2

So on the top I get:
m x m²s^-2

and on the bottom I get

m kg s^-2 m² kg^-2

all the m and the s cancel so i just get the kg left

So what! You haven't even told us what the equation is so why should we care what the units are?

Actually it's not even an equation because it doesn't have an equals sign. How is anyone to know what is right or what is wrong with just one side of the equation?

 

[Mute]

OK, I must be wrong before I get that far.

I have:

m x (ms^-1)²
N m² kg^-2

So on the top I get:
m x m²s^-2

and on the bottom I get

m kg s^-2 m² kg^-2

all the m and the s cancel so i just get the kg left

So you get
$$\frac{1}{kg^{-1}} = kg.$$

Is that what you're supposed to get? Without knowing more details we can't say anything more than that the units of what you started with in this post work out to kg.

 

[PonderingMick]

So you get
$$\frac{1}{kg^{-1}} = kg.$$

Is that what you're supposed to get? Without knowing more details we can't say anything more than that the units of what you started with in this post work out to kg.

Yes that's right, this means that my calculation is correct because the answer is a mass.

But I still don't understand why the answer to this is kg:

$$\frac{1}{kg^{-1}} = kg$$

 

[PonderingMick]

Ok, I get it now:


$$\frac{1}{kg^{-1}} = kg$$

for the same reason that
1
10^-1 = 10

Thanks