Scientific American presents Math Dude by Quick & Dirty Tips. Scientific American and Quick & Dirty Tips are both Macmillan companies.

In the last Math Dude episode, we learned the ins and outs of rounding numbers. And, hopefully, we learned (or were reminded) that rounding numbers is pretty easy. But as it turns out, that's not exactly true—because there are a few tricky situations when it's not.

What are they? Here's a hint: They have something to do with the number 5. How do you deal with this pesky number 5? And does this ever matter in the real world? Those are exactly the questions we'll be answering today.

How to Break Rounding Ties
When it comes to rounding numbers, the only real question is which way to round the number 5. In other words, how should we break a tie? For example, if we want to round π = 3.14159 to the thousandths place (that's the second 1 in 3.14159), do we round up to get 3.142? Or do we round down to get 3.141? As we found out last time, the rule of thumb is to round up.

But why exactly do we do this? Well, I'm sorry to have to break this to you, but the truth is that there really isn't a deep reason for all of the rounding up we do. The simple truth is that 5 is right smack-dab in the middle, which means that there isn't one and only one correct way to do it. However, since we do ultimately have to go one way or the other, we need to make a choice—and rounding up is the convention that has been adopted most broadly.

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