Rounding decimals on the number line

- [Instructor] So we are asked to drag the point to 12.5 on the number line, so let's see. Let's see, this is 12, and 12.5 is halfway between 12 and 13 then say say what is 12.5 rounded to the nearest 10? Well, what's cool about this is you can see on the number line that our tens are in this blue hash. So we have 10 and then 20 and we're between 10 and 20 and which one are we closest to? Which is literally the nearest 10? Well, you can see we are closer to 10 than we are to 20 so you would say 10, and this helps us build an intuition for what rounding to the nearest 10 even means because you might know a rule like, hey look, you go one place less than the tens place, which would be the one's place and if it's less than five there you round down to 10. If it's five or greater you round up to 20. But you see why over here, we are just closer to 10. Let's do another example here. So here it says drag the point to 0.136. So this is 0.13, this is 0.14, so this is 13 hundredths and this is 14 hundredths, now let's see. There's one, two, there, four, five, six, six, seven, eight, nine, ten. So these are, you could think of it as the ten thousandths between these two hundredths. So we want to go 13 hundredths and then another six thousandths. So let's see, we go one, two, three, four, five, six. Just like that, and then they say what is this number? 136 thousandths or 0.136 rounded to the nearest hundredth. Well, we have our hundredths in blue here, and which one are we closer to? Well, we're closer to 14 hundredths, 0.14. And that's consistent with what we've seen in other cases where you look at the thousandths place and if it's five or greater you round up. In this case, you would round up to 14 hundredths. Let's do a few more examples here. So let's say that, so they're asking us which point is at 44.197 on the number line? So let's see, that's going to be between 44 and 45, so it's right over here, 44.197, so that would be point C. And then they say, what is 44.197 rounded to the nearest whole number? Well, there's a couple of ways to think about it. You could just look at the tenths place and say look, that's less than five so we round down to 44 or a more intuitive way of thinking about it is like look, point C is the number we care about. That is 44.197. What's the closest whole number to it? Is it closer to 44 or is it closer to 45? Well, it's clearly closer to 44, so that's another reason why 44 makes a lot of sense. Let's do another example. Let's say that we want to, so they say, what is A rounded to the nearest thousandth? What is A rounded to the nearest hundredth? So A is right over here, let's get our bearings. So 0.7, that's seven hundredths. This is eight hundredths right over here. And then between them, let's see, this looks like it's zero, so you can view this as 70 thousandths, 71 thousandths, 72 thousandths, 73 thousandths, 74 thousandths, and so on. So this is between 78 thousands and 79 thousandths. So if we round to the nearest thousandth it looks closer, in fact, it's definitely closer to 78 thousandths than it is to 79 thousandths. So I would say this is 0.078, or 78 thousandths. That's closer, that's the nearest thousandth. What is A rounded to the nearest hundredth? Well, what are the hundredths that it's in-between? It's in-between seven hundredths and eight hundredths. And which one is it closer to? Well, it's closer to eight hundredths, 0.08. So once again, the whole point of this video is to appreciate when people say round to the nearest whole number, to the nearest 10, to the nearest thousandth, to the nearest hundredth, you can think of it on a number line and just say, well, what is the closest hundredth to it? Or what hundredth is it closest to? Which thousandth is it closest to on the number line?