I need to measure out 70 ml of liquid.
I have a 10 ml measuring cylinder with a maximum uncertainty of 0.1 ml and a 100 ml measuring cylinder with a maximum uncertainty of 1 ml.
I've calculated that using the 10 ml cylinder 7 times would give a 0.7 maximum uncertainty, or a 0.7/70=1% percentage uncertainty. Meanwhile, using the 100 ml cylinder, I get a 0.1 ml uncertainty, or a 1/70=1.4% percentage uncertainty. Clearly, the smaller cylinder approach is more accurate (1% < 1.4%)
Meanwhile, the mark scheme says that one must use the 100 ml cylinder, for the 10 ml cylinder would give a total 7*0.1/10=7% percentage uncertainty, compared to the 1.4% from the 100 ml cylinder. (1.4% < 7%)
Isn't adding percentages in this way fallacious? There's no way to accumulate a 4.9 ml error using a 10 ml cylinder 7 times, right? I'd appreciate if someone could clarify which approach is correct and why.