There are actually laws about how old a child must be before he or she can be left alone legally. I would caution on this side of things.. if ever something were to happen while you were gone, it could be considered child abusse for leaving your child alone too early in life..
check into it before you start to make those decisions. I have run down to the corner newstand to pick up a paper and told the kids I was doing this first.. and that was okay.. but I wouldn't really go to the market for a full grocery shop yet.. I have an 8 year old too.