Rounding decimals on the number line
So we are asked to drag the point to 12.5 on the number line. So let's see. You can see this is twelve, and then twelve point five is halfway between twelve and thirteen. Then they say, what is twelve point five rounded to the nearest tenth?
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 ten and then twenty, and we're between ten and twenty. Which one are we closer to, which is literally the nearest ten? Well, you can see we're closer to ten than we are to twenty. So you would say ten. This helps us build an intuition for what rounding to the nearest ten even means. Because you might know a rule like, "Hey look, you go one place less than the tens place," which would be the ones place. If it's less than five there, you round down to ten. If it's five or greater, you round up to twenty. But you see why over here we are just closer to ten.
Let's do another example here. So here it says drag the point to zero point one three six. So this is zero point one three; this is zero point one four. So this is 1300s, and this is 1400s. Now let's see, there’s one, two, three, four, five, 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 thirteen hundreds and then another six thousandths. So let’s see, we go one, two, three, four, five, six, just like that.
Then they say, what is this number 136 thousandths or 0.136 rounded to the nearest hundredth? Well, we have our hundreds in blue here, and which one are we closer to? Well, we're closer to 1400s, 0.14, and that's consistent with what we've seen in other cases where you look at the thousandths place. 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 forty four point one nine seven on the number line. So let's see, that's going to be between 44 and 45. So—right over here—44.197, so that would be point C.
Then they say, what is forty four point one nine seven 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 5, 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 point one nine seven. Is it close? 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, and 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. Like, let’s get our bearings.
So zero point seven—that seven hundredths—this is eight hundredths, right over here. And then between them, let’s see, this looks like it’s zero. This is—so you could view this as seventy thousand, seventy one thousand, seventy two thousand, seventy three thousand, seventy four thousandths, and so on. So this is between 78 thousandths and seventy nine thousandths.
So if we round to the nearest thousandth, it looks closer—in fact, it’s definitely closer to seventy eight thousandths than it is to seventy nine thousandths. So I would say this is zero point zero seven eight, or 78 thousandths—it’s closer; that’s the nearest thousandth.
What is A rounded to the nearest hundredth? Well, what are the hundreds 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 ten, 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?