# When expressing a quantity, do the non-significant figures determine whether you round up the last significant figure?

I had thought that the non significant figures determined whether the least significant figure was to be rounded up. For example, given the number $9.1145$, if the number is to be expressed as three significant figures, then, I had thought that, it would be expressed as $9.12$.

However, I noticed that in one of my chemistry professor's calculations in which the quantities were expressed as significant to three figures, she expressed $8.125 \times 10^2$ as $813$. In another calculation she expressed $9.1145 \times 10^{-3}$ as $0.00911$. However, it seems to me that $0.00912$ is the correct expression of $9.1145 \times 10^{-3}$, as the $5$ requires rounding up the $4$, which requires rounding up the least significant $1$ to $2$.

Is there a rule for rounding that my professor is following that I don't know?

(Note: this isn't a homework question, but the homework tag seemed to be the most appropriate one.)

• Never round twice. If that was the rule, then 0.46 could be rounded up to 1, which is clearly not the case. – HDE 226868 Oct 4 '15 at 19:04
• Relevant meta discussion – M.A.R. Oct 4 '15 at 19:55