# Precision and accuracy of a solution

1. Apr 5, 2015

### cham

1. The problem statement, all variables and given/known data
so let's say that we have a solution S=0.4±0.01/250ml
i want to do a dilution
so i pick 5ml and pour it into 100ml beaker
how should i calculate precision of the solution (mathematically or with some other equations)?
2. Relevant equations
so basically we have F=5*S/100

3. The attempt at a solution
for me 5*S/100=8*10^-5±2*10^-6
is this true because it doesn't seem right for me (about the pricision)?

Last edited: Apr 5, 2015
2. Apr 5, 2015

### Staff: Mentor

The relative uncertainty stays the same, that is right.
You might get an additional uncertainty if the 5ml or the 100ml are not exact.

3. Apr 5, 2015

### cham

so
so what you say is that no mater how many dilution we do the precision stays the same and it depends on the solution we're using.so it means ±0.01 for all diluted solutions we made,right?

4. Apr 5, 2015

### Staff: Mentor

The relative uncertainty stays the same.
It is always 1/40. Roughly speaking, your solution might be 1/40 more concentrated than you thought, or 1/40 less. And that uncertainty does not change if your dilution factors afterwards are known exactly.

5. Apr 5, 2015

### cham

so let's assume that final result is true , so it would be 8*10^-5 ±1/40 and so for all resulting solutions
and that by using Δy/y
correct me if I'm wrong
thanks and sorry for my stubbornness

6. Apr 5, 2015

### Staff: Mentor

I am afraid you can be sure neither 5 mL nor 100 mL are exact and they are additional sources of error.

7. Apr 5, 2015

### Staff: Mentor

No, in this case it would be 8*10-5 +- 2*10-6 as the uncertainty is 1/40 of the value.

With the caveat that the 5ml and 100ml won't be exact, as mentioned.

8. Apr 6, 2015

9. Apr 6, 2015

### cham

thank you mfb and Borek for your help
much appreciated

10. Apr 6, 2015

### Staff: Mentor

You can use @cham to tag users in the thread.