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Comparing multi-digit numbers

CCSS.Math:

Video transcript

compare ninety-eight thousand nine hundred eighty nine and ninety-eight thousand eight hundred ninety nine 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 nine all the way to the right or in the ones place value which it means just that it means nine 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 eight we have a nine in the hundreds place value so again we can look at that 989 is the same as a nine hundred plus an eighty plus a nine 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 ninety thousand plus eight thousand plus nine hundred plus 80 plus nine 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 so when we compare these numbers we're going to can 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 has 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 I just 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 and our first number on the Left we have 900 900 but on the right we have eight hundreds so eight hundreds is less than 900 s so 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 ninety-eight thousand nine hundred eighty nine is greater than ninety eight thousand eight hundred ninety nine 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 can pair 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 fifty-three thousand and three hundred fifty thousand 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 play 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 are actually comparing 300,000 to 50,000 those are two different place values we want to compare hundreds thousands two 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 three hundred thousand 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 zero and then compare so to read this will say 53,000 is less less then 350,000 and this symbol is less then 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