If you're working and able to apply at other places then your foot is already in the door. Getting a job when unemployed is the hard part. The moment you're able to get a better job - take it.
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Would you like fries with th... I mean, your milk in a bag?
If you're less than 6 months you need not put it on the resume.
I highly suggest to stay a minimum of 1 year with any company. It looks better on the resume.
I know several people who have a long laundry list of jobs and it isn't uncommon for them to have had 30+ jobs since high school. The fewer the better on the resume in the long run. Even if it's a garbage job I stay a minimum of 5 years; 3 if it's really bad. Some people don't mind the constantly changing jobs, always being at risk of waking up one day and could be without a job. Others like me don't like that feeling so a unionized job that offers job protection is helpful. I can not tell you how many jobs I've woken up to and was fired before I even got to work because someone decided they didn't like me and fired me for some b.s. reason. Only to find out it was a half a$$ed **** and bull lie. Or go on 2 weeks vacation only to find out on vacation they terminated you because they didn't have the guts to tell you in person.
That's just enough time for Kroger to hire you, schedule you for a once-a-month class without telling you, schedule you for work without telling you, and then fire you for not showing up to a job they never told you about.
If the managers are literate, one month. If not, two.