The height of josie’s dog 11 1/4 inches to the nearest quarter inch and 11 inches to the nearest half inch. which measurement is more precise

Both measurements are correct if you're rounding the dogs height.

But the more precise measurement would be 11 1/4.

Mainly because its a smaller fraction so it has more meaning to it instead of just plain 11

It would get more precise as the fraction got larger
For example.

Not very precise 
11, 11 1/2, 11 1/4,   

Precise
11 1/8, 11 1/16 

Hope this helps!
Brainliest is always appreciated if you feel its deserved!

For range i think it’s area