Question

suppose your professor handed you a test tube with 2.0 mL of broth culture in it and told you to make a 10^-1 dilution of entire culture, how?

Answer 1

use the formula c1*v1=c2*v2 (which is initial concnetration times initial volume = final concentration times final volume).
we know that v1=2.0 mL. we know that c1=1 (or 100% if you prefer to work in percent). we know that the final concentration should be 10^-1, so c2=10^-1=0.1(or 10% if you use percentage). so we are just searching for v2 (the final volume)

1 *2 (ml) = 0.1 * v2 (ml)
so
2=0.1*v2
multiply both sides by 10 to get:
20=v2 (ml)
so we know that the final volume will be 20 ml, so to actually make the solution, you will need to add enough water to your 2 ml of broth to make the finalvolume 20 ml.

so 2 + (amount of water needed)=20
so amount of water you need to add to your 2ml of broth = 18ml.