Comparing multi-digit numbers
- [Voiceover] Compare 98,989 and 98,899. So we want to compare these two numbers and to do that, let's first think about what these digits mean. What do these numbers actually mean? Looking first at our number on the left, we have a 9 all the way to the right, or in the ones place value, which means just that. It means nine ones. Beside that, we have an 8 in the 10s place value, so that's eight 10s or 80. This number, these two right here, 89 is the same as an 80 plus a 9. Beside the 8, we have a 9 in the 100s place value, so again, we can look at that, 989 is the same as a 900 plus an 80 plus a 9 and let's keep going and fill in these last two. We have an 8 in the 1,000s place, and finally, a 9 in the 10,000s place, which means nine 10,000s or 90,000, so 98,989 is the same as 90,000 plus 8,000 plus 900 plus 80 plus 9. Which of these place values now seems like the most important one if we're deciding how big a number is? Which one of these has the biggest impact on the size of our number? And the answer is the one all the way to the left, whatever place value is farthest to the left is the greatest place value, so it is the most important in deciding how big or how small a number is. So when we compare these numbers, we're going to start by comparing the largest place value that either of them has. In this case, 10,000s is the largest place value both of them has, and in both cases, it's a 9, so both of these numbers start with 90,000 which is equal, we can't tell yet which one is greater, so we're going to move to the next biggest place value. The next largest place value is the 1,000s and again, we can see in both cases, we have an 8 or 8,000, so looking at what we've compared so far, these numbers are identical, neither is larger than the other, so we're going to keep going and again, we're going to pick the next largest place value, which is the 100s and our first number on the left, we have nine 100s, nine 100s, but on the right, we have eight 100s, so eight 100s is less than nine 100s, so this number on the right is less than our first number, the number on the left, or we could say, the 900 is greater than 800 so the number on the left is greater and this is our greater than symbol because we want the open side to be facing the larger number. We want the open side facing the larger number. So we'd read this as 98,989 is greater than 98,899. And you might be thinking, but wait, we didn't look at the 10s and look at the 10s. Here, we have eight 10s, but on the right we have nine 10s. Well, nine 10s is definitely greater than eight 10s but it doesn't make up for having less 100s. 100s are far bigger, 10 times bigger, than 10s, so they matter more, they had a bigger impact on which of these numbers was larger. So, we compare until we find the greatest place value that's different and then whichever of those has the greater number in that place value is the greater number. Let's try one more. So here we're comparing 53,000 and 350,000. At a quick glance, you might be thinking, okay, first number 5, first number 3. The highest place value is bigger here, it's a 5. But that's not quite enough. We still have to be sure we're comparing the same place values. This largest place value here, this 5, is in the 10,000s place. But the largest place value over here, the 3, is in the 100,000s place. So we are actually comparing 300,000 to 50,000. Those are two different place values. We want to compare 100,000s to 100,000s, so looking over here, how many 100,000s did this number have? And the answer is a great, big zero. It has zero 100,000s, so we can say zero 100,000s and when we compare that to 300,000, that's far less. No 100,000s is much less than three 100,000s, so actually, this second number is larger, so be careful not just to compare the first number but the largest place value, and if there's no digit in that place value, we can fill in a zero and then compare. So to read this, we'll say 53,000 is less, less, than 350,000, and this symbol is less than because the larger side is open to the bigger number and the bigger number is the second number, so 53,000 is less than 350,000.