Most most monitors (since more than 10 years), if they notice they don't get a signal from the computer any more, show a message like "No signal" and turn into a low power stand-by state. Physically turning off with the power off button can even lower the power used.
Since all monitors are different, even from the same manufacturer, check the user manual if this is automatic, or if you somehow have to enable it in the monitor menu.
how can I program my monitor to my computer so that it will shut down when I turn off the computer. I am working with windows 7 and have a dell computer with an Acer monitor

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