How to Round Numbers (Part 1)

How do you round an integer like 723 to the nearest tenth? How about rounding a decimal number like 3.14159 to the nearest hundredth? Is rounding numbers ever actually useful in the real world? Keep on reading to find out!

Jason Marshall, PhD,
September 7, 2013
Episode #165

Round NumbersAt some point in your life, you were most likely taught how to round integers and decimal numbers to some specified number of digits or decimal places. And you probably discovered that this process is, thankfully, fairly straight-forward.

But even though it is a relatively easy task, it turns out there are a few details about rounding that make it a touch trickier than you might at first think. What are those tricky little bits that you really ought to know about? And how do you round in the first place? Those are exactly the questions we'll be answering over the next few weeks!>

Why Is Rounding Useful?

Imagine this: You need to put together a monthly budget for your company that sells novelty T-shirts depicting cats dressed as baristas. You decide that the best way to get started is to take a look at all of your company's expenses over the past 6 months, and to calculate the average monthly cost of each kind of expense. Perhaps your average cost for the shirts themselves turns out to be $1,024, the average cost of shipping turns out to be $512, and the average monthly cost of all the fancy coffee drinks you buy to inspire you when drawing your barista cats turns out to be $128.

After doing all of these calculations, you realize that these numbers are kind of a pain to deal with. After all, do you really need to know the average cost of each thing to the nearest dollar? Isn't that a tad more precise than what you actually need? Mightn't it be good enough to know all of your costs to something like the nearest $10 instead? Absolutely! Which is why rounding $1,024 to $1,020, rounding $512 to $510, and rounding $128 to $130 is a great idea in this case since these "round" numbers will make your calculations a little simpler. And the slight loss of precision doesn't really matter.

As we'll find out in a couple of weeks, the idea of significant figures might mean that we actually want to round these numbers even further. But let's not worry about that just yet. For the time being, what you really need to know is that sometimes it's helpful to round numbers to some level of precision. By which I mean to some specified number of digits—to the nearest $10 in our case.

When Not to Round

It's also good to keep in mind that sometimes you really, really don't want to round the numbers in a calculation if you don't have to—if you're doing super-precise calculations that are going to be used to help land a rover on Mars, for example. Or maybe when doing some sort of calculation that's going to be used to help determine how to engineer and build a skyscraper. In high-stakes situations like these, rounding numbers could wind up turning your billion dollar project into a sad heap of rubble—so it's highly advisable to keep every last bit of precision you can. We'll talk more about this idea of precision in the coming weeks.

In the meantime, now that we know why we might want to round numbers, it's logical to ask: How do you actually do it?

How to Round Integers

As I said before, thankfully it's pretty easy to round numbers. Here's how it works: To round a whole number to some digit—such as the tens or hundreds—all you have to do is look at the digit to the right of the one your rounding to. If that digit is less than 5, then you round down; if that digit is 5 or greater, you round up.

What do I mean by round "up" and "down?" It's easiest to see with a few examples. Let's say we're trying to round 723 to the nearest 10. To do so, we need to look at the digit immediately to the right of the 2 that's in the 10s place of 723. In other words, we need to look at the 3 in the 1s place. Since 3 is less than 5, we round 723 down to 720. What if we were instead rounding the number 727 to the nearest 10? In that case, since the number in the 1s place is 7 (which certainly is greater than or equal to 5), we need to round 727 up to 730. That's really all there is to it.

How to Round Decimal Numbers

How about decimal numbers—are they any more difficult to round? Nope, the idea is exactly the same. For example, let's say we're trying to round 3.14159 to the nearest hundredths place (you might recognize this as the beginning of everybody's favorite irrational number, π). As you'll recall, the hundredths place is the second digit to the right of the decimal point—that's the 4 in 3.14159. To round to the nearest hundredth, we therefore need to look at the digit immediately to its right—in other words, the 1 in the thousandths place. Since that number is less than 5, we need to round down—which gives us a rounded value of pi equal to 3.14.

Occasionally, instead of being told the particular value of the digit you need to round to, you'll instead be asked to round your answer to something like 4 decimal places. What does that mean in terms of π? Well, the 4th decimal place of π contains the number 5. Since the digit to the right of 5 in 3.14159 is 9 (which is greater than or equal to 5), we need to round up—which means that π rounded to 4 decimal places is 3.1416.

Once you've got this basic idea down, you'll find that it doesn't matter if you're dealing with integers or decimal numbers, rounding is a straight-forward process. Straight-forward, that is, until you run into one of the sticky situations we'll be talking about next time. Be sure to check back to find out exactly what those sticky situations might be! 

Wrap Up

Okay, that’s all the math we have time for today.

Be sure to check out my mental math audiobook called The Math Dude’s 5 Tips to Mastering Mental MathAnd for even more math goodness, check out my book The Math Dude’s Quick and Dirty Guide to Algebra.

Remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too. Finally, please send your math questions my way via FacebookTwitter, or email at mathdude@quickanddirtytips.com.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

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Round numbers graphic from Shutterstock.

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