Which measurement in more precise 54.1 cm or 54.16 cm

The measurement 54.16 cm is more precise by virtue of the fact that it contains more information than the measurement 54.1 cm.

Let's think about this for one moment...

54.16 contains five tens, four ones, one tenth, and 6 hundredths.

54.1 contains five tens, four ones and one tenth.

From the above information you can deduce that the value 54.16 contains more information than the value 54.1.