That is the correct spelling of the plural noun "errands"
(tasks, chores).
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I'll be running errands for the rest of the day.
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no
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The expression is not idiomatic. It means exactly what it says.
To be sent on ( or for) errands means to be out on a shopping trip,
or such like, for someone.
Mother sent me on errands to the grocery store and the dry
cleaners.