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Rounding to nearest 10
Throughout your mathematical life, you will find situations where you will need to round numbers. And you might be saying, well why? What situations might that be? Well, these would be situations where you're trying to get an estimate on things. Where you're trying to-- maybe you have a measurement and you want it to be a little bit less exact to simplify things. Or you don't trust how exact the measurement is. So here we're going to actually think about what rounding is. And we're going to round each of these numbers, 36, 34, 35, 26, and 12. We're going to round each of them to the nearest 10. And I'll give you a hint of what that means. That essentially says take each of these numbers, and find the multiple of 10 that it is closest to. So what are multiples of 10? Well, 10 times 0 is 0, 10 times 1 is 10, 20, 30, 40, 50, 60, so on and so forth. So I encourage you to pause this video, and just based on what I just told you, what is the nearest multiple of 10 to each of these numbers? Try to think about that. Well, to think about it a little bit deeper, let's actually put a number line here. I'll put two number lines over here. So we've got some number lines here. And let's think about where these points would sit on this number line. So this first number, 36, where does it sit on this number line? Well, it's between 30 and 40. And this little blue mark is 35, it's halfway between. So 36 is going to be a little higher than that. So 36 is going to be right over here. And if we zoom in between 30 and 40. So if we say that this is 30, and this is 40, where is 36 going to be? So once again, this is 35. 36 is one notch above that. So 36 is going to be right over here. So if we want to round to the nearest 10, to the nearest multiple of 10, what are the two possibilities here? Well, I could take 36 and I could round up to the multiple of 10 above it, which is 40. So I could round up to 40, or I could round down to the multiple of 10 below it, which is 30. And so I need to figure out which of these numbers is it closer to. Well, when you just look at that, even just eyeballing it, you can see it. But you could also say 36 is only four away from 40, and it's six away from 30, it's closer to 40. So we are going to round up. We are going to round up to 40. This is literally called rounding up. Now let's try some of these other numbers. What about 34? And I encourage you to pause the video. Think about what number you would get if you were to try to round it up or round it down, and then which one it is actually closer to. Well, 34 is right over here on this number line, where we zoom in, 34 is right over here. And we have two options. The multiple of 10 above 34-- let me do those same colors-- the multiple of 10 above 34 is 40. Multiple of 10 below 34, again, is 30. Now, which one is it closer to? Well it's only four away from 30, and six away from 40, so it's closer to 30. So we are going to round down to 30. And notice we went to 30. You might say, hey, when we rounded it up the 10's place increased from 3 to 4, from 30 to 40. Maybe when we round down, the 10's place will decrease from 30 to 20, but no, 30 is the multiple of 10 below 34. So when you round down, you just go-- you keep the multiple of 10, but the ones place becomes a 0. Now let's try a really interesting one. Let's think about rounding the number 35 to the nearest 10. And first, before we even try to do it, let's think about the two options. Well, we've already seen it. 35 is sitting right over here. On this number line, that is 35, and once again we have two options. 35, we can round it up to 40, or we could round it down to 30. And I encourage you to pause the video and think about this. Well this one is a little bit of a conundrum because it's five away from both elements. It's five away from 40, and five away from 30. So the mathematical community has decided to define what to do in the case where you have a 5 in the ones place. If you have five or more in the ones place, you will round up. This is just a rule. Five or more in the ones place, you round up. So 35, you round up to 40. Notice, a 6 in the ones place was five or more. So if you're rounding to the nearest 10, you round up to 40. A 4 in the ones place is not 5 or greater, so we rounded down. And so this gives a pretty good clue for these other two numbers. Let's try-- let's see what happens with 26. 26, what are the two options? What is a multiple of 10 above 26, and what is a multiple of 10 below 26.? Well, the multiple of 10 above 26 is 30, and the multiple of 10 below 26 is 20. So if we round up, we go to 30. If we round down, we go to 20. Well, if we're rounding to the nearest 10, we look at the 10's place. That's what we're going to round-- we're going to round to the nearest 10-- but then we look at the ones place. The ones place is going to decide it. And we see here this is 5 or greater. Or you could say this is greater than or equal to 5. So we round up. 26 rounded to the nearest 10, we round up to 30. Now what about 12? And I think you're getting the hang of this. Well let's think about the multiple of 10 above 12. So we could either round up to 20. So 12 is sitting right around here. We either round up to 20 or we round down to 10. Well, if we're going to round to the nearest 10, we have to look at the ones place. We have to look at the ones place right over here. This is less than 5. Since it's less than five, we round down, which makes sense because it's also closer to 10 than it is to 20. So we round down, and rounding 12 to the nearest 10, you actually get 10.