anonymous one year ago 22.4 kg/L to kg/ml please work out so I can unsderstand

1. YoloShroom

Hey there, britt , still need help?

2. anonymous

yes

3. YoloShroom

Alright so, every 1 kg/l equals .001 kg/ml so to get how many kg/ml we need, we mulitply 22.4 by .001, can you do that for me?

4. anonymous

Basically we want the L's to cancel out so that we can keep the units of kg, but convert L to mL. Basically, $\frac{ kg }{ L }*\frac{ L }{ mL }$

5. YoloShroom

or you can do that.

6. anonymous

|dw:1444174080721:dw|

7. anonymous

right ?

8. anonymous

I always found it easier to construct this sort of "table" of units first to see what direction I need to go. Once you have the units set up as I did above, then plug in what you know. $\frac{ 22.5kg }{ 1L }*\frac{ .001L }{ 1mL }$

9. anonymous

Still lost

10. anonymous

can you guys draw it out make that could help

11. anonymous

there are 1000 ml in one Liter thus one could say $$\bf \cfrac{1000ml}{1L}\quad or\quad \cfrac{1L}{1000ml}\qquad thus \\ \quad \\ \cfrac{22.4kg}{\cancel{1L}}\cdot \cfrac{\cancel{1L}}{1000ml}$$

12. anonymous

so, you use, whatever fraction of the unit, that's convenient in this case, the L is at the bottom, so the convenient fraction is the one with the L atop, so it cancels out the one at the bottom

13. anonymous

I'll try to dissect this to make it easier to grasp. We're initially given that we have $\frac{ 22.4kg }{ L }$ But we want the L to become mL. Well how do we do this? We know that for 1L, there are 1000mL. That is the definition of mL. Another way to represent this relationship is to say that that 1mL is 0.001L. This means that 1mL is a thousandth of a L. Given this relationship, we can convert L to mL by multiplying by the conversion that we just stated AKA 1000mL in 1L. Therefore: $\frac{ 22.4kg }{ L }*\frac{ 1L }{ 1000mL }$ is the "table" or equation that we need to solve the problem. Does this make sense?

14. anonymous

yes

15. anonymous

Okay perfect. The rest is easy :) By multiplying, we get$\frac{ 22.4kg*L }{ 1000mL*L }$ Oh look, the L's cancel out Therefore, after dividing our numbers and units, our final answer is$0.0224\frac{ kg }{ mL }$

16. anonymous

This makes sense that we can an even smaller number than before. Think of this - you have 5 cookies, even spread across 5 plates. How many cookies are on 1 plate? 1.

17. anonymous

omg i get it |dw:1444175148409:dw|

18. anonymous

Exactly! :) These sort of tables are always helpful when doing math with units and converting them.

19. anonymous

thanks please stay online haha i kinda get it now.

20. whpalmer4

$1000 \text{ mL} = 1 \text{ L}$As one of the other posters mentioned, we have L but want mL. Divide by the unit we don't want: $\frac{1000\text{ mL}}{1 \text{ L}} = \frac{1\text{ L}}{1\text{ L}}$ $\frac{1000\text{ mL}}{1 \text{ L}} = \frac{1\cancel{\text{ L}}}{1\cancel{\text{ L}}}$ $\frac{1000\text{ mL}}{1 \text{ L}} =1$ We can always multiply something by $$1$$ and we just get the same thing back. This is a special version of $$1$$ that will allow us to convert units. $22.4 \text{ kg/L} = \frac{22.4\text{ kg}}{1 \text{ L}} = \frac{22.4\text{ kg}}{1\text{ L} * (\frac{1000 \text{ mL}}{1\text{ L}})} = \frac{22.4\text{ kg}}{1\cancel{\text{ L}} * (\frac{1000 \text{ mL}}{1\cancel{\text{ L}}})}$$=\frac{22.4\text{ kg}}{1000 \text{ mL}} = \frac{0.0224\text{ kg}}{\text{mL}}=0.224 \text{ kg/mL}$ By doing it in this fashion and carefully canceling units, you get built-in error-checking. If the units end up weird, you've almost certainly done it incorrectly.

21. Hero

The other way to do it

22. Hero