Question

convert 37.5 g/mL to kg/L

Answer 1

Hint: m = .001, k = 1000

Answer 2

I'll be back in a sec

Answer 3

Okay, basically change the milli and the kilo to their actual numerical values first

Answer 4

\[\frac{37.5 g}{.001 L} = \frac{\text{____} 1000 g}{L}\]

Answer 5

Actually, you can probably make that blank an x

Answer 6

After cross multiplication and manipulation, you'll end up with:

\[\frac{37.5 g}{x 1000 g} = \frac{.001 L}{L}\]

Answer 7

Now, to cancel out those annoying variables that make things more difficult than they have to be:

\[\frac{37.5}{x 1000} = \frac{.001}{1}\]

Answer 8

Now, .001 is the same as 1/1000, so we can re-write the other side as:

\[\frac{37.5}{x 1000} = \frac{1}{1000}\]

Answer 9

Cross multiplication and manipulation leads us to this:

37.5 = x

Answer 10

You probably did not understand anything I did

Answer 11

dimension analysis method is simpler i think

Answer 12

Maybe, but this works too.

Answer 13

It depends on the person. Dimensional analysis is useless for me

Answer 14

Thus,

37.5 g/mL = 37.5 kg/L

Answer 15

Yeah, I'll probably just try Dimensional analysis. But thanks to all who contributed! (:

Answer 16

Dimensional analysis is tons simpler and more dynamic:
\[37.5\frac{g}{mL}\times \frac{1kg}{1000g} \times \frac{1000mL}{1L}=37.5\frac{kg}{L}\]

Answer 17

I don't know about the "more dynamic" part.

Answer 18

If you look at what I did more closely, you'll realize how simple my way is as well.

Answer 19

The only reason my steps appear longer is because of my attempts to explain the methods I used.

Answer 20

I would just like to say that I too think dimensional analysis is not a more effective way to solve these problems. I find that dimensional analysis makes thing more complicated than they should be.

Answer 21

I know this does not actually answer the question, but I just felt the need to input my opinion.

Answer 22

How do you deal with converting complicated products of units with your system? Like:\[k_e=8.988 \times 10^9 N \cdot m^2 \cdot C^{-2}\]Besides setting up several proportions.

Answer 23

You didn't tell me what to convert it to

Answer 24

It's not impossible