Video: Ordering Given Large Numbers in Descending Order

Arrange 77613970, 718701545, 392434430, 762816353 in descending order.


Video Transcript

Arrange 77613970, 718701545, 392434430, and 762816353 in descending order.

When we arrange something in descending order, this means we start with the largest and we get smaller and smaller. It’s the order from largest to smallest. Now, if we read our question, we can see that we have four different numbers. Each of the numbers has at least eight digits. Three of them have nine. And there are commas within each number and also separating the numbers. So, if we look quickly at the question, it might just look like a string of digits. How can we compare these numbers and put them in order?

Well, a good way for us to do this is by writing the numbers vertically, and we can use a place value grid to help us do this. The largest of these numbers, as we’ve already said, has nine digits. So, we need to make sure that our place value grid has nine columns. The lowest value of these columns is the ones column. To the left of that we know is the tens column, then the hundreds column. We can call the hundreds, tens, and ones our ones section. The next three columns we can call our thousands section. We have the thousands column, ten thousands column, and hundred thousands column. And our final group of three digits are the millions. We have the millions column, tens of millions, and hundred millions.

Now, we’ve created our place value grid. Let’s write each number vertically in there. 77 million, 613 thousand, 970. Onto our second number, 718 million, 701 thousand, 545. Our third number is 392 million, 434 thousand, 430. And the last of our four numbers is 762 million, 816 thousand, 353. Now, as we’ve said already, to arrange these numbers in descending order, we need to look for the largest number first. And so, the column we need to be looking at is the hundred millions column. It’s the column with the largest value. Which number has the largest value digit in this column? Well, we can see, two numbers have the largest digit. They both have seven. We can’t split them up.

So, now we need to move on and compare the digit with the next largest value, and that’s the tens of millions digit. In the first of our two numbers that we’re looking at, there’s one lot of ten million. But in the second of our two numbers, there are six lots of ten million. And six is greater than one. And so, we can say that the last number on our list should actually be the first number if we’re writing the numbers in descending order. It’s the largest of the four numbers. So, let’s begin by writing out that number, 762816353.

Now that we’ve worked out the largest number, the other three numbers are very straightforward to put into order. We know that the second largest number must be the number we were just looking at, 718701545. We know this because it’s the other number that has 700 million in it. And out of our two remaining numbers, it’s easy to see which is largest.

The first number that we’re looking at doesn’t have any hundred millions. In fact, it’s an eight-digit number, not a nine-digit number. And so, we know the larger of the two numbers must be 392434430. And so, the first number in our original list is actually the last number if we put the numbers in descending order. It’s the smallest number. And so, if we arrange these numbers in descending order, the order is 762816353, 718701545, 392434430, and finally 77613970.

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