Plotting decimal numbers on a number line

- [Voiceover] We're asked to move the orange dot to 5.90 on the number line, or you could view this as 5 90/100, or 5 9/10. All right, so let's see, this is 5.8, and then this is 6.0. One way to think about it is 5.9 is exactly halfway between 5.8 and 6.0, and this is written as 5.90, but we could view this as 5.9, so it's going to be exactly halfway. Now, one interesting thing to think about is what do each of these tick marks represent? Well, if this is 5.8, and if 1/10 higher than 5.8 is 5.9 over here, and then 1/10 higher than that is 6.0, so from here to here is 1/10, and then from here to here is another 1/10. Then they've divided each 1/10 into one, two, three, four, five, six, seven, eight, nine, 10 sections, so each of these represent 1/10 of 1/10, or 1/100, so for example, this would be 5.81, 5.82, 5.83, 5.84, 5.85, 5.86, 5.87, 5.88, 5.89, 5.90. So either way, I think we got it. All right, let's keep doing some more of these. Move the orange dot to 2.87 on the number line. All right, this is interesting. So, this is 2.8. That's 3.0. Halfway in between would be this longer hash mark, or this longer tick mark, right over here. This would be 2.9. So 2.87, this is just like we saw in the last example. Each of these is 1/100, so this is 2.8, this would be 2.81, 2.82, 2.83, 2.84, 2.85, 2.86, 2.87, and we could just check. This would be 2.88, 2.89, 2.9, or 2.90, which is exactly halfway between 2.8 and 3.0, so I'm feeling good about that. Let's check our answer. We got it right. You know, after you get a question right, it doesn't hurt to look at the hints at that point, so let's just see how they tackled it. So, they say, "Above we've drawn "the number line from 2.8 to 3.0," and they divided into 20 equal pieces. Yup, that looks right. Let's see their next hint. So, they say that piece of the line is 3.0 minus 2.8. That's gonna be 2/10, and then you divide by 20, is 0.1. So, that's another way that they're just saying that, "Hey, each of these is 1/100," but we already saw that. 2.81, 2.82, 2.83, 2.84, 2.85, 2.86, 2.87. Let's just do another one. The hints actually, I think, keep going after that. So (mumbles) I encourage you to look at the hints. See if you can make sense of them after you try the exercise. So, let's try another one. Let's do one more. Move the orange dot to 0.27 on the number line. Well, this is 0.2, this is 0.3, so going from here to here is 1/10, and then they've divided that 1/10 into 10 sections, so each of these is 1/10 of 1/10, which is 1/100. So, this is 2/10 and 0/100, 2/10 and 1/100, 2/10 and 2/100, 2/10 and 3/100, 2/10 and 4/100, 2/10 and 5/100, 2/10 and 6/100, 2/10 and 7/100. This is 2/10 and 7/100. Another way you could view it is, this is 20/100. 2/10 is the same thing as 20/100. 21/100, 22/100, 23/100, 24/100, 25/100, 26/100, 27/100. All right. Check our answer, and let's just see the hints. They say "10 equal pieces." They show us that right over here. They actually labeled it. Anyway, hopefully this helps. I encourage you to go try this exercise out now.