How to divide large bank notes into smaller ones while traveling?

I try to pay for each purchase using only the next larger denomination. That way I end up with plenty of change.

Paying for a 1200 rupee hotel? Use 2x 1000 rupee notes.
Paying for a 120 rupee taxi? Use a 500 rupee note.
Paying for a 15 rupee bottle of water? Use a 20 rupee note.

In Japan, Japan Post Bank ATMs give 1,000 and 10,000 yen bills only. You can request arbitrary amounts of each, and the bills to be dispensed are displayed for confirmation before the transaction is complete.

The easiest way to request 1,000 yen bills when withdrawing an amount which is a multiple of 10,000 is to use the 千 (1,000) button instead of or in addition to the 万 (10,000) one. For example if I want to withdraw 10,000 yen as ten 1,000 yen bills, I type １０千 instead of １万. Likewise, if I want to withdraw 40,000 yen as two 10,000s and twenty 1,000s, I type ２万２０千.

Small shops are usually reluctant to take large notes at the beginning of the day, because they start with a limited amount of cash to make the change. Once they’ve had a few customers, they usually have enough money in the cash register to accommodate you.

So, if you have troubles paying a shop with a large note, you should simply try again later, sometimes just letting a few people make their purchases ahead of you. Asking the shop by what time they expect to have enough change also helps.

If you want to make purchases in vending machines, simply look around: there might be a special terminal which makes the change. Those are installed together with vending machines to improve the sales.

Some ATM’s in Western Europe ask you what denomination you prefer. If that is not the case, I usually try to do some mental arithmetic and withdraw an amount which cannot easily be factored by whatever large denominations exist in the foreign country. Say, for example, you are in the Euro Zone and want to avoid €50 notes. You can withdraw an amount that cannot easily be factored by €50. Federico Poloni gives a practical example here for Euros:

Example: most European ATMs give out 20 and 50 Euro notes. Withdraw amounts ending in 80 or 30 (such as 80, 130, 180, 230, 280… Euros) to ensure you have at least four 20E notes.

Obviously, withdrawing say €80 can result in various combinations, including €50 + €20 + €10. This method is therefore not bulletproof, although it ensures that you will get a combination of denominations, including small bills.

Some strategies:

• Take less out of the ATM. It may dispense different denominations and
  give you smaller notes if you only ask for a little money. This, of
  course, may backfire on you if you have to pay an ATM fee, since the
  fixed fee will add up to a higher percentage of the money taken out.
  But if you have a free ATM (or one where only a percentage-based
  foreign transaction fee applies), it’s a worthwhile strategy.

• Similarly, if you know what denominations the ATM dispenses (if it offers multiple denominations), you can be strategic when deciding how much to withdrawal to force it to give you at least some smaller bills. It’s not always easy to know what foreign ATMs give out though.

• Larger, higher-end hotels can often make change at the front desk or
  restaurant (in part because people need change to tip the hotel
  staff). This is intended for their guests, though they may be
  accommodating if you walk up to the front desk and generally look
  like you could be a guest.

• There may be a staffed ticket window (for trains or public transit)
  that can accommodate larger bills than the ticket machines.
  Alternatively, pay for your tickets with a credit card.

• You don’t need to make an unnecessary purchase of overpriced goods to
  get change. Some shops may be willing to make change without a
  purchase (though often not), but you can always buy an inexpensive
  beverage, pack of gum, or a small snack and pay for it with a large
  bill. This gives you change and something refreshing or tasty. If you
  ask the clerk to change another bill at this time (before he/she has
  the register open), they may be able to accommodate you.

• Grab a drink at a bar. You get a delicious drink and your change. If
  the bartender expects a tip, he/she will make sure you get small
  bills back as part of that.

• Try at a bank. Whether banks will make change for
  non-customers will depend on the country and bank policy. You may
  have better luck if you tell the bank you just got the money from
  their ATM.

• If you’ve been there before, bring some small notes home and bring
  them back next time. This can be a useful strategy for a currency you
  don’t mind holding and are likely to use again, less so for an
  unstable currency or one from a place you’re unlikely to return.

• As you travel, you can keep an eye on your small bill supply and
  ensure it is topped up by using larger notes even when you have
  smaller ones available. This means you primarily only have to really
  worry about this problem at the very beginning of your trip.