Place value with decimals

What we're going to do in this video is refresh our understanding of place value, but we're going to dig a little bit deeper and think about place value in the context of decimals.

So just as a refresher, if I had the number 973, this should be review for you. We already know that this rightmost space right over here, this is the ones place. And if we move one space to the left of that, this is the tens place. Notice we went from ones to tens. Tens are ten times as much as ones.

Then we move one space to the left of that. We go to the hundreds space. And so this nine doesn't just represent nine; it represents nine hundred. Or we could write that as nine hundred. Similarly, the seven doesn't just represent seven; it represents seven tens or 70. This three represents three ones, so it actually does represent three.

But as I promised, we're now going to extend our understanding. What we do is we put a decimal here, which you've probably seen before, at the right. The reason why we even need a decimal is to really tell us where our ones place is. We say, okay, if we go right to the left of the decimal, that's going to be our one space.

Because once we start introducing decimals, we can introduce as many spaces as we want to the right of the decimal. And so, let's think about those a little bit. When we went from hundreds to tens, notice we divided by ten. When we go from tens to ones, notice you divide by ten.

So what do you think this place over here is going to be called? Well, what happens if you take 1/10? Well, then you get 1/10. So, as you might imagine, this is the tenths place. Then if you were to go one place to the right of that, what would this place be? What would be tenths divided by ten or one tenth of a tenth?

So this would be the hundredths place. And then if you were to go one space to the right, and we could keep doing this forever, but if we were to go one space to the right of that, what would it be? Well, a hundredth divided by ten, or one tenth of a hundredth, is the thousandths place.

And so, for example, if I were to extend this number instead of it just being 973, if I were to write nine hundred seventy-three point five two six, what do these numbers, these digits, represent? This five doesn't just represent five; it represents five tenths.

Or another way of writing five tenths, you could write it like this: zero point five. You just have a five in the tenths place, or you could write it as five tenths. This two—and I think you get where this is going—this doesn't just represent two; it represents two hundredths.

I'm just going to make it very explicit in this video, so it's very clear: two hundredths. Another way to write that is you just write a two in the hundredths place, so we're going one, two spaces to the right of the decimal, or you could write it as two over a hundred—two hundredths.

And so, you know, for kicks, pause the video. What are all the different ways of representing this six? What does this six represent? Well, this is six thousand.

There you go! How would I? I could also write that as zero point, let's use the tenths place, hundredths place, and then in the thousandths place, I have six. Or I could write this as six over one thousand—six thousandths.

So big picture: place value, we can keep going to the right of the decimal, and we can start representing things that are, I guess you could say, more precise.