Please, if possible, check if my method of dilution is correct

Problem: Given a very concentrated liquid PBS, dilute it to 1:15,000

My approach is to use serial dilution
First: dilute it 15x (50ul of PBS + 750ul of water)... this will give 1:15

Second: dilute 10xfold more (100ul PBS from step 1 + 900ul water)...this will give 1:150

Third: dilute anotehr 10x fold more (100ul PBS from step 2 + 900ul water)...this will give 1:1500

Fourth: dilute anotehr 10x fold more (100ul PBS from step 3 + 900ul water)...this will give 1:15000

Is my approach and calculation correct?

I saw this and didn't want to try and help because their is a lot of math involved for something so simple, and I believe that is why others have ignored it. The simple way to do this is to scale up because this, in my opinion, is a complicated process to achieve a 1:15,000 dilution. Take 10uL of sample and dilute it with 150,000uL of solvent, or 150mL of water. There are 1,000uL pipettes and just do that 15 times and vortex the thing for 30 seconds. That way you save reagent, and the systematic error that is associated with that many dilutions, in my opinion, is kind of high. Also, if you have a 1 to 5uL micropipette, take 1uL of sample and add 15mL of water; scale up as needed depending on how much of the concentration you need.

Yes, your approach and calculation for the serial dilution seems to be correct.

To dilute the concentrated liquid PBS to a ratio of 1:15,000, you have correctly performed a series of dilutions.

In the first step, you are diluting 50 μl of the concentrated liquid PBS with 750 μl of water. This gives you a dilution factor of 1:15 (50 μl/750 μl = 1/15).

In the second step, you are taking 100 μl from the dilution in the first step and adding 900 μl of water. This gives you a dilution factor of 1:150 (100 μl/900 μl = 1/9 = 1/15 * 1/10).

In the third step, you are again taking 100 μl from the previous dilution and adding 900 μl of water. This gives you a dilution factor of 1:1500 (100 μl/900 μl = 1/9 = 1/150 * 1/10).

Finally, in the fourth step, you take 100 μl from the dilution in the third step and add 900 μl of water. This gives you the desired dilution factor of 1:15,000 (100 μl/900 μl = 1/9 = 1/1500 * 1/10).

So, according to your description, your approach and calculation for the dilution is correct.

Your approach to perform a serial dilution is correct. Each step involves diluting the previous dilution by a factor of 10. However, there seems to be a slight mistake in your calculations. Let's break it down step by step:

Step 1: Dilute 15x
You correctly stated that you need to mix 50 μl of PBS with 750 μl of water. This will result in a final volume of 800 μl. This step gives you a dilution of 1:16, as you started with 50 μl of PBS and ended up with 50 μl/800 μl = 1/16.

Step 2: Dilute 10x from step 1
Here, you should take 100 μl from the diluted solution in step 1 and mix it with 900 μl of water. The final volume will be 1000 μl, resulting in a dilution of 1:16 * 1:10 = 1:160.

Step 3: Dilute 10x from step 2
Similar to step 2, take 100 μl from the solution in step 2 and mix it with 900 μl of water. This yields a final volume of 1000 μl and a dilution of 1:160 * 1:10 = 1:1600.

Step 4: Dilute 10x from step 3
Once again, take 100 μl from the solution in step 3 and mix it with 900 μl of water. The final volume will be 1000 μl, resulting in a dilution of 1:1600 * 1:10 = 1:16,000.

So, technically, your calculations were very close but just one step ahead of the required dilution of 1:15,000. Therefore, you need to perform one more dilution step to achieve the desired dilution.