Try calling market’s manager or asking for “Книга жалоб и предложений” where you can leave a note on not serving you because of change. These notes can be used later for fining the cashier or the whole firm. According to laws the cashier is just showing dishonesty by not serving a person which have enough money to buy something.
I worked as a cashier for 4 months and we could easily find a solution for this problem: we had a lot of change since opening and even in case it wasn’t enough, the cashier could take yesterday’s change.

There is a joke on that: можно заламинировать пятитысячную купюру и использовать как проездной в транспорте :)

Not only for foreigners :) As far as I know, most people working in large companies get paid to their plastic cards and therefore get cash from ATMs. Some are paying with those cards in supermarkets, but most people still prefer using cash.

There is an additional problem as well for us foreigners in Russia nowadays, and that is that ATMs are the easiest way to get money. The банкоматы usually issue 1000-ruble notes, for which indeed sometimes cashiers simply do not have the change. I was very pleased when I found a банкомат that mostly issued 500-ruble notes, and now I try to use it regularly. Cashiers deal with those rather better.

Asking for exact amount is coming from Soviet times. Not exactly this habit but an overall position of the service personnel. In USSR, service workers was standing on the higher level of hierarchy than ordinary people (sounds weird now but it’s true) because they had access to limited resources. The situation has changed now but peoples’ minds haven’t changed so much. So most cashiers in supermarket think they are standing higher than you, and some customers think so, too. Personally I always feel some kind of guilt when I don’t have enough change to please them. I guess it needs a couple of generations to change.

This is a wonderfully practical and accurate post! I wish that when I was an undergraduate, my cohort had received this kind of basic information before we went to Russia. In Дикси, the chain supermarket I frequented in Petersburg, cashiers invariably asked, ‘Карта есть?’(referring to some kind of loyalty card, I think) and then, ‘Пакет нужен?’. If you answered yes to the latter, the next question was even more penetrating: ‘Большой или маленький?’ There never seemed to be a ‘средний’, although that was what I always needed. And yes, I learned to carry bags на случай (although in England, where I live, supermarkets also charge for bags, so the habit was ingrained).

Perhaps you could post some advice on coping with Russian cashiers’ often peremptory and inflexible demands for exact change? Or how to keep the small talk flowing while you search for 38 kopecks under the glare of six overburdened housewives queuing behind you?

Don responds: You’re not just whistlin’ “Dixie.” (Sorry, couldn’t resist ) The request for exact change comes not just from cashiers in stores, but also taxi drivers and restaurants and bookstores. I’m not sure if this is a function of the national money supply being limited, or just the habit of businesses not to stock more change.

No advice for dealing with the glare… except maybe “grin and bear it"?