# What does it mean to take reading up to 0.05 mL?

In titration we usually take burette reading upto $0.01~\mathrm{mL}$, but my teacher says that we need to take reading up to $0.05~\mathrm{mL}$. What does that mean? Does it mean if I read $23.56~\mathrm{mL}$ that I should record it as $23.60~\mathrm{mL}$ and if I read $23.44~\mathrm{mL}$ I should record it as $23.40~\mathrm{mL}$?

I believe what your teacher means by this is that the error for your measurement is within $0.05~\mathrm{mL}$ of the estimate, since $0.05~\mathrm{mL}$ is half the value of the smallest measurable volume in a typical $50~\mathrm{mL}$ burette. This is typically how the error of an instrument reading is determined.
The readings you gave would then be: $23.56~\mathrm{mL} \pm 0.05~\mathrm{mL}$ and $23.44~\mathrm{mL} \pm 0.05~\mathrm{mL}$.