Comparing multi-digit numbers | Math | 4th grade | Khan Academy

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 9 ones. Beside that, we have an eight in the tens place value, so that's eight tens or eighty. This number, these two right here, eighty-nine, is the same as an eighty plus a nine.

Beside the 8, we have a 9 in the hundreds place value. So, again, we can look at that; 989 is the same as 900 plus 80 plus 9. And let's keep going and fill in these last two. We have an eight in the thousands place and finally a nine in the ten-thousands place, which means nine ten-thousands or ninety thousand.

So, ninety-eight thousand nine hundred eighty-nine 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 small a number is. When we compare these numbers, we're going to start by comparing the largest place value that either of them has. In this case, ten-thousands is the largest place value both of them have, and in both cases, it's a nine.

So both of these numbers start with ninety thousand, 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 thousands, and again, we can see in both cases we have an eight or eight thousand. 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 hundreds. In our first number on the left, we have nine hundreds, but on the right, we have eight hundreds. So, eight hundreds is less than nine hundreds.

Thus, this number on the right is less than our first number, the number on the left, or we could say that 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 tens." And look at the tens; here we have eight tens, but on the right, we have nine tens. Well, nine tens is definitely greater than eight tens, but it doesn't make up for having less hundreds. Hundreds are far bigger, ten times bigger than tens, so they mattered 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 a 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 five, first number three; the highest place value is bigger here; it's a five." 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 five, is in the ten-thousands place, but the largest place value over here, the three, is in the hundred-thousands place. So we're actually comparing 300,000 to 50,000. Those are two different place values; we want to compare hundreds, thousands to hundred-thousand.

So looking over here, how many hundred-thousands did this number have? And the answer is a great big zero. It has zero hundred-thousands. So we can say zero hundred-thousands, and when we compare that to 300,000, that's far less. No hundred-thousands is much less than three hundred-thousands.

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 0 and then compare. So to read this, we'll say 53,000 is 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.