Today, I bought some stuff that totaled $128.58. I gave the cashier $140. Unfortunately, she hit the wrong key and entered $1.40. She wasn't flustered, but simply proceeded to figure out the change she owed me. She obviously wasn't afraid of a little arithmetic, and I had correct change a few seconds later.
What struck me was that she had apparently never tried giving change by counting up. Some of you may be shaking your heads at this point, especially if you ever worked a cash register in your youth. But perhaps by now you have kids of your own.
So you're working at the cash register. A customer buys $17.23 worth of stuff, and hands you a twenty. How much change do you owe him? Think about it before continuing.
The correct answer is who cares? Well, the customer cares, and the manager cares, but you don't. Counting up is a way to give correct change without actually bothering to figure out how much it is.
Let's say I've bought $7 worth of stuff and handed you a ten-dollar bill. Start at $7, and count up to $10 by dollars, each time pulling a dollar bill out of the cash register: "8 (pull out a dollar), 9 (pull out a dollar), 10 (pull out a dollar)."
Notice that you've pulled out three bucks, which is exactly how much you owe me. You could've figured out that you owed me $3, then counted out "one, two, three," but you get the same result if you just count "eight, nine, ten."
But people's totals don't usually come out to nice, round numbers. More often you'll wind up with a total of $11.43 out of $50. Not a problem. You just count out pennies until you get to a multiple of five cents. Then you count out nickels until you get to dimes, then quarters, dollars, five dollars, and so forth.
So let's say the total comes to $32.33 and the customer hands you $50. Start by counting out pennies: "34 (pull out a penny), 35 (pull out a penny)."
Since 35 cents is divisible by 5, move on to nickels. Starting from 35 where you left off, count out "40 (pull out a nickel)."
40 is divisible by 10, so you can move on to dimes: "50 (pull out a dime)."
50 is divisible by 25, so you move on to quarters: "75 (pull out a quarter), 33 dollars (pull out a quarter)" (remember, you were counting up from $32 all this time, so when you go up from 75 cents, you're really going up from $32.75 to $33).
Now continue with dollar bills: "34 (pull out a dollar), 35 (pull out a dollar)."
35 is divisible by 5, so you continue with five-dollar bills: "40 (pull out a fiver)." Then ten-dollar bills: "50 (pull out a tenner)."
With any luck, you figured it out three paragraphs ago, and skipped down here. The one other thing to remember is that you can skip denominations: if the customer buys something for 47 cents and hands you a dollar, you start by counting "48 (penny), 49 (penny), 50 (penny)."
Now, 50 is divisible by both 5 (nickels) and 10 (dimes), but it's also divisible by 25. So skip the nickels and dimes, and go directly to quarters: "75 (quarter), one dollar (quarter)."
Okay, so why do you care about this? Well, computerized cash registers are wonderful, but sometimes they don't work, or you might make a mistake and mess up the display. The customer's not likely to be terribly sympathetic, so the best thing to do is to get him out of your hair quickly. And like most people today, you probably don't want to do more mental arithmetic than you have to. Counting up is simple, it works, and it gives the right result even when you don't know what it is.