Decimals on the number line
Use a number line to compare 11.5 and 11.7. So let's draw a number line here. And I'm going to focus between 11 and 12, because that's where our two numbers are sitting. They're 11, and then something else, some number of 10ths. So this right here is 11. And this right here would be 12. And then let me draw the 10ths. So this would be smack dab in between. So that would be 11 and 5/10, or that would be 11.5. Well, I've already done the first part. I've figured out where 11.5 is. It's smack dab in between 11 and 12. It's 11 and 5/10. But let me find everything else. Let me mark everything else on this number line. So that's 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, and then 10/10, right on the 12. It's not completely drawn to scale. I'm hand-drawing it as good as I can. So where is 11.7 going to be? Well, this is 11.5, this is 11.6, this is 11.7. 11 and 7/10. 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10. This is 11.7. And the way we've drawn our number line, we are increasing as we go to the right. 11.7 is to the right of 11.5. It's clearly greater than 11.5. 11.7 is greater than 11.5. And really, seriously, you didn't have to draw a number line to figure that out. They're both 11 and something else. This is 11 and 5/10. This is 11 and 7/10. So clearly, this one is going to be greater. You both have 11, but this has 7/10, as opposed to 5/10.