Turning off your LED computer monitor does save a bit of energy but the new LED computer monitors use very little electricity that it's hardly noticeable on the electric bill when they are on all the time.
Turning your computer monitor on and off too much can wear the computer monitor out faster than just leaving it on all day.
If I'm going to bed for the night or leaving the house for longer than an hour I will turn the computer monitor off and then turn it back on when i get back or wake up.
But if I'm gonna be home all day and need to use the computer or plan to use the computer through the day I just leave the computer monitor on.
The average LED computer monitor uses around 20 to 25 watts of electricity per hour which is very little compared to the old CRT monitors that used 80 watts to 100 watts per hour.
So that means that my LED computer monitor if kept on for 10 hours per day uses around 250 watts per day or 7,500 watts per month.
Since my KWH cost is 10 cents per KWH it costs me around 80 cents for the month to keep the led computer monitor on which is a very low cost.