Rounding Decimals: How To Know Which Way Is Up

rounding decimalsRounding decimals may seem a little tricky if you don’t know the positions or the basic rules, but it’s really very simple. And it’s worth knowing how to do it the right way, because it can make a real difference when you’re dealing with money.

Speaking of money, if you’re concerned about numbers and finance — personal or business — there’s quite a variety of online classes that you might want to check into.

What It’s All About

OK. Let’s start with the basics. When we talk about rounding a number, what do we mean?

Basically, if you have a number that’s a long string of digits, and you don’t want to mess with all of them, you can round it off. The trick is that the farther to the right you go, the actual value of each digit gets smaller (9 is a lot less than 200), so when you’re dealing with a long string of digits, the digits on the far right end are usually not that important.

Game-Show Arithmetic

Imagine you’re a contestant on a game show, and the game-show host tells you that if you answer the next question correctly, you’ll win $1,000,000.17, but if you get the answer wrong, you’ll only get $1,000,000.02. Are you going to worry too much about getting the answer right? You’ll probably spend a lot more time worrying about whether you’re just asleep and dreaming the whole thing, because the actual difference between the winning prize and what you’ll get if you lose is only fifteen cents — either way, you’ll still walk away with a million dollars. That fifteen cents just isn’t very significant.

Toss It Out

And that’s just what you do when you round off numbers. You decide (based on what you’re going to be doing with the number) how far to the right you have to go before the numbers stop being significant, then get rid of all of the numbers to the right of that point. Here’s an example: You start with 123,456, and decide that anything smaller than 1,000 isn’t significant, so you toss out the 456, which gives you 123,000. Pretty easy, isn’t it?

Up Or Down?

But wait! Not all numbers are the same. Like these, for example: 5,999 and 5,001. The first number is just a tiny bit short of being 6,000, while the second one is barely more than 5,000. It wouldn’t seem right to round them both off to 5,000, would it?

And it probably wouldn’t be right, either. You can round numbers up (so the rounded number is just a notch higher than the original) or down (so the rounded number is a notch lower). A little bit of common sense would tell you that you should round 5,999 up to 6,000 and 5,001 down to 5,000 in most situations.

Splitting the Difference

With numbers like 5,999 and 5,001, it’s pretty easy to see what to do, but what about these numbers: 14,261 and 14,875? If you want to round them off to the nearest 1,000 (by throwing out everything to the right of the comma), do you round them both to 14,000? It makes sense to just get rid of 261, but 875 is kind of on the high end — not that far from 1,000. Do you throw it out as well, or round the whole number up?

As it turns out, there’s a rule that tells you when to round numbers down or up. Take a look at the highest digit that you’re going to throw out. If it’s less than 5, you round down. if it’s 5 or more, you round up. With 14,261, the highest digit of the ones that you’re going to toss out is the 2 in 261, which is lower than 5, so you get rid of it, and round the number down to 14,000. With 14,875, the highest digit of the part that you’re going to eliminate is 8, which is higher than 5, so you keep it, and round the number up to 15,000.

Let’s Get Small

Decimals are pretty easy: divide 1 by 10, and you get 0.1, which is one tenth (1/10). Divide 1 by 100 to get 0.01, or one hundredth (1/100). Divide 1 by 1,000, and you have 0.001, which is one thousandth (1/1,000). (See that 0 to the right of the decimal point? It’s just there so the decimal point won’t get lost when you look at it. Otherwise, you can ignore it.) To find the size of a decimal place, just count to the right of the decimal point: tenths, hundredths, thousandths, ten-thousandths, hundred-thousandths, millionths, etc.

Don’t Sweat the Small Stuff

As you can already see, you don’t have to go very far to the right before the numbers are so small that they’re hardly there at all. (OK. If you’re doing precision engineering or scientific research, numbers like 0.0001 or even 0.0000001 may be important. But even engineers and scientists stop worrying about the numbers when they get small enough.)

Have Another Round

Let’s take some of the numbers that we were using before, shrink them down to decimal fractions, then round them:

For example, if you want to round 1.23456 off to the nearest thousandth, you’d count out to the thousandths’ place (that’s where the 3 is) and knock off everything to the right: 1.23. What about 5.999 and 5.001? You’d probably round them like you would the large versions, to 6 and 5, respectively.

And if you want to round both 1.4261 and 1.4875 off to the nearest tenth (where the 4 is), you’d follow our earlier example, rounding the first number down to 1.4, and the second one up to 1.5. What if you wanted to round them to the nearest thousandth? As it turns out, you’d round them both up, because the digits in the places just to the right of the thousandths (6 and 7) are both greater than 5, so you’d get 1.43 and 1.49.

Need To Know More?

Those are the basics of rounding decimals, and of rounding numbers in general. The right way to round numbers is a useful thing to know for personal finance, for business, for such diverse fields as cooking, carpentry, and machining, and for any field where you may need to work with numbers.