Theory:

If a rational number pq,q0 can be expressed in the form of p2m×5n, where p and m,nW, the rational number will have terminating decimal expansion. Otherwise, the rational number will have non-terminating and recurring decimal expansion.
Example:
Verify the following have terminating decimals or non-terminating and recurring decimal expansion.
 
1. 120
 
120=14×5=122×51.
 
Thus, the given rational number follows the pattern p2m×5n.
 
Therefore the number 120 have terminating decimal expansion.
 
 
2. 42625
 
42625=4254=4220×54.
 
Thus, the given rational number follows the pattern p2m×5n.
Therefore the number42625 have terminating decimal expansion.
 
 
3. 19225
 
19225=199×25=1932×52.
 
Thus, the given rational number does not follow the pattern p2m×5n.
 
Therefore the number 19225 does not have terminating decimal expansion. It has a non-terminating and recurring decimal expansion.
 
 
4. 37350
 
37350=372×25×7.
 
 
37350=3721×52×71.
 
Thus, the given rational number does not follow the pattern p2m×5n.
 
Therefore the number 37350 does not have terminating decimal expansion. But it has a non-terminating and recurring decimal expansion.