Decimal Place Values: Getting Them Straight

decimal place valueDecimal place values are actually pretty easy to understand. They may have given you trouble in the past, but once you see what’s really going on, we think you’ll see how easy they really are.

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One and One and One and One…

Let’s start with a quick review of what happens with number on the left side of the decimal point  —  the side where the large numbers are.  And we’ll start right at the beginning, with 1.

“Well, that’s pretty obvious,” you say, “after all, 1 is just 1.”  And you’re right, but there’s more to it than that.  One is the most basic number in any practical system of everyday arithmetic  —  every other number is just adding up, multiplying, or dividing ones.

It’s Just A Jump To the Left

Move 1 a single space to the left (and put a zero where it was), and you’ve got 10, which is ten times larger. Move it another space to the left, and you’ve got 100, which is 10 times 10.  Another space to the left gives you 1,000, which is 10 times larger than 100.  And it just keeps going on like that.  (Notice the commas. They divide the places (or digits) into groups of three.  Every time you see a group of digits with a comma, the number to the left of the comma is 1,000 times larger than the number to the left of the previous comma, like this: 1,000,000 is 1,000 times larger than 1,000, or to put it another way, if you have 1,000 piles of 1,000 bricks, you have 1,000,000 bricks.)

And A Step To the Right

But what about those numbers to the right of the decimal place?  Those are the ones that you’re probably concerned with the most.  Not only don’t they have any commas, but you can’t even use them to count bricks.  As a matter of fact, you can’t even count one brick using the numbers to the right of the decimal place  —  at least not unless you used a sledge hammer to smash the brick into little pieces first.  But pounding on a brick with a sledge hammer is messy, and it’s hard to keep track of the pieces, so let’s cut up a pizza instead.  It’s a big pizza, but you’ve got plenty of hungry friends, so we’re going to have to do a lot of cutting.

Fun With Pizza

Let’s start with a not-too-big crowd.  You’ve got one pizza (you ordered “The Big One,” so we’ll call it 1), and you have to divide it between ten people, so you cut it into ten pieces (we’ll let you figure out the best way to do that).   If the pizza is 1, then each piece is 0.1 pizza.

What does that mean?  If you were to use a regular fraction, you’d say that each piece is 1/10 pizza  —  one tenth of a pizza, since it’s cut into ten pieces.  0.1 is just another way of saying 1/10.  (Notice the 0 to the left of the decimal? You don’t really need to put it there, since it doesn’t make any difference in the value of the number, but most people do, because it makes it easier to notice the decimal.)

So why don’t people just use traditional fractions? As it turns out, for most purposes, it’s actually easier to do arithmetic with decimal fractions  —  and many of the fractions that pop up in real-life situations are very unwieldy when you write them out in the traditional format.

The Party Gets Bigger

But back to the pizza. More friends have shown up  —  a lot more, and suddenly, you’ve got to divide the same pizza between not ten, but 100 people!  What do you do?  The pizza’s already cut into ten pieces, and since 10 x 10 = 100, if you cut each of those pieces up into ten smaller pieces, you’ll have 100 (very small) slices of pizza. Each slice is 1/100 pizza. How would you write that as a decimal fraction?  That’s right  —  0.01 pizza.

You’re about to serve your guests their tiny slices of pizza, when without a warning, the entire neighborhood drops in to visit.  That makes 1,000 people total.  They’ve heard you’re serving pizza, and they all want a slice.  10 x 100 = 1,000, so you start cutting up each of those 100 very small slices of pizza into ten even smaller pieces. What fraction of a pizza is each slice?  1/1,000 pizza.  And what decimal fraction does that make? 0.001 pizza. Not enought to even get stuck in your teeth!

The Numbers Get Smaller

At this point, it should be clear that the farther to the right of the decimal point you go, the smaller the fractions get, and that they get small very quickly.  That turns out to be a very important point.  Suppose you have to deal with a number like this:  0.251302178751875090245278.  That looks pretty bad, doesn’t it?  But it really depends on what you need to do with it.  If you’re doing some kind of ultra-precise engineering calculation, maybe it needs to be accurate to one part in 1,000,000. That is very precise, but it means that you can round it off to the 1/1,000,000 place, and throw out all the numbers to the right of that (because they’re too small to count).  Rounding it off gives you 0.251302.

But They Also Get Easier

What if you’re cutting small pieces of ribbon, and you want them to be very close to each other in length, but not that precise  —  one part in 1,000 accuracy is fine.  Then you can round it to 0.251.  And what if you just need to roughly estimate a measurement?  You can call it 0.25, and if you know how some of the most common traditional fractions convert to decimal fractions, you’ll recognize 0.25 as 1/4.

In other words, that ridiculously long and difficult 0.251302178751875090245278 turns out to be just a tiny bit over 1/4  —  close enough for cutting pizza.

Numbers are important in just about every part of life, and there’s a lot that you can learn about them.  You can find online classes in personal finance, business finance, spreadsheets, intro to algebra, or just plain getting out of debt.