Place value and decimals are related. We can begin by reviewing the concept of ones, tens, and hundreds places, and then demonstrates how tenths, hundredths, and thousandths places work. By understanding place value, we can interpret the meaning of each digit in a decimal number.
- [Instructor] 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 have 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. And then we move one space to the left of that, we go to the we multiply by tens again. We get to the hundreds space and so this nine doesn't just represent nine, it represents nine hundred or we could write that as 900. 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 and what we do is we put a decimal here which you've probably seen before at the right and 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. If 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 one divided by ten? Well then you get a tenth so as you might imagine this is the tenths place. And then if you were to go one place to the right of that, what would this place be? Well it'd be tenths divided by ten or 1/10 of a tenth, so this would be a hundredth, hundredths place. And then if you were to go one space to the right 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 1/10 of a hundredth is a thousandth, thousandth space. And so for example if I were to extend this number instead of if just being 973, if I were to write 973.526, 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 0.5 you just have a five in the tenths place. Or you could write it as five tenths. This two 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 100, two hundredths. And so for kicks, pause the video what are all the different ways of representing this six? What does this six represent? Well this is six thousandths, six thousandths, thousandths, there you go. I could also write that as zero point, let's see it's the tenths place, hundredths place, and then in the thousandths place I have six or I could write this as six over 1000, 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.