For reasons not entirely clear to me, gas is reliably 40-70¢ a gallon less expensive in the town where I work, 30 miles north of home, than it is in the stations right by home. Sam's club, which I dislike going to unless it's at an off time, is 10 miles out of the way and somewhere between the two.
If I find myself low over the weekend, I will often stop at the station closest to my house and buy 2-3 gallons on Sunday night or Monday morning. That will get me to work with plenty to spare(which take 1-1.25 gallons) and then I fill up as I'm leaving work on Monday.
If I run down to 1/4 tank, it will take me about 14 gallons to fill up. Using actual current prices, if I buy 3 gallons at the station by my house($3.89) it will cost me 11.67. I'd probably put $10 or $15 in and call it a day, but let's say for the sake of this that I did exactly 3 gallons. Filling up would cost me $54.46 at this station.
If I put 3 gallons in, drive to work and really luck out on stop lights and driving perfectly, I'll need 12 gallons to fill up. Realistically, in this scenario, it's probably going to be more like 12.5 gallons, but we'll go with the smaller number. Current price at the station closest to my work is $3.29, so that tank will cost me $39.48.
My total spent on gas for the day is now $51.15, and so I've saved $3.31 AND ended up with an extra gallon of gas vs. filling up close to home. Neither stop takes me out of the way, and probably adds 10 minutes to the day.
I don't find myself in that specific scenario all that often-maybe once every other month. I usually try to fill up by work at the end of the week, and it's rare that I will use enough gas over the weekend that I feel I need to fill up before going to work on Monday. Even at that, though, 6 times a year means an extra hour of my time over the course of the year and saving probably close to $40. It's small but in my mind probably worth it.
Of course, I COULD probably chance it and make it to work on 1/4 tank. I've done it before, and it was fine. The main people traveling my direction in the morning are people headed to where I work, and traffic jams are rare but do happen(and lately I have had an occasional construction delay). Still, though, running out of gas would certainly mitigate any potential savings from pushing it. In the above scenario, if I did risk it, using the same basic numbers I'd pay $49.35 for a full tank and, again, get an extra gallon of gas. That's about $5 saved vs. filling up at home, or about $2 less than the way I usually do it(a small amount close to home). The $2 is worth not worrying about running out.
Then there's the extra-alternate scenario where I have a gallon or two lawnmower gas in the garage that probably should be cycled out for fresh, so I gather that up dump it in my tank. I do that with careful consideration, though, since most of what I keep on hand is 32:1 pre-mix. I'd not worry about adding that to a nearly full tank, but am not sure about one so close to empty. Least often touched, though, is the can I keep designated for "pure" gas since I don't have any 4 cycle outdoor equipment currently and it's mostly there just as a backup that I can mix if I'm in the middle of mowing and find myself out of gas.