Finding the nearest multiple of 1,000, 10,000 and 100,000

0:00- [Instructor] We're told for the number 372,590, what is the nearest multiple of 100,000? And they give us a little bit of a blanket number line here, we have some other questions here, but the way that I'm gonna do it is I'm going to think about what multiples of 100,000 is this number in between, and then I'm gonna try to roughly see where it sits on that number line.

0:25So for example, for 372,590, the hundred thousands place is right over here. So this number is between 300,000 and 400,000. So let me write that here. This is 300,000, for this point on my number line, and I'm gonna make this one, 400,000. Now the number 372,590, where would that be on this number line?

0:53Well, if it was 350,000, it would be right over here. 372,000 is a good bit further, it'd be something like right over here. So if we wanna say what is the nearest multiple of a hundred thousand, we just have to say, okay, is this where I put 372,590? Is it closer to 400,000 or is it closer to 300,000?

1:15Well, we can clearly see it is more than halfway of the way from 300,000 to 400,000. So the nearest multiple of a hundred thousand is 400,000. Now that is an example, why don't you try the next one? What is the nearest multiple of 10,000? Alright, so here we're going to do something very similar, but instead of saying multiples of a hundred thousand, we're gonna think about multiples of 10,000 and the ten thousands place, And maybe I'll do this in a new color just for a little bit of variety.

1:43We have seven ten-thousands in that 70,000 or 72,590. So if we go to the nearest 10,000, below this number, we are going to be at 370,000. And the nearest 10,000 above this number is going to be 380,000. Now, where does 372,590 sit? Well, if it was 375,000, it would be right in the middle.

2:11So 372,590 is going to be someplace around there. So what's the nearest multiple of 10,000? Well, we're definitely not even halfway of the way between 370,000 and 380,000, we're definitely closer to 370,000, so that's what I would write. Let's do this last example, maybe in green.

2:35What is the nearest multiple of a thousand? Once again, pause this video. Have a go at it before we do this together. So once again, let's look at the thousands place. So if we go to the nearest thousand that's below this number, it would be 372,000. And then the nearest thousand, that or multiple of a thousand that's above this would be 373,000.

2:58Notice these numbers are a hundred thousand apart. These numbers are 10,000 apart. These numbers are a thousand apart. And so where's 372,590? Well, 372,500 would be right in the middle, but 372,590 is more than halfway. It's going to be roughly right over there, so you can see that it's closer to 373,000 than it is to 372,000.

3:24So we would go right over there. You might be wondering, what if we were right in the middle? What would we say we are nearest to? Well, you might make an argument that we're equally near to either end, but as you go further in your math career, you'll learn that when people wanna think about this, they come up with certain rules when you are stuck in that tie-like situation.