19/23 ≈ 0.826086956521739
Rounding that to the nearest hundredth means you look at the 6 to the right of the hundredth place
0.826086956521739
Since 6 is closer to 10 than 0, you round the 2 up to 3.
0.83
Another way to describe that is that 26 (taking both the 2 and 6 into account) is closer to 30 than it is to 20.
0.826 is closer to 0.830 than 0.820