# Question Video: Ordering Decimal Numbers in Descending Order Mathematics • 5th Grade

A furniture store is displaying four tables. The lengths of the tables are 5 feet, 5.202 feet, 5.2 feet, and 5.26 feet. Arrange the tables’ lengths in descending order.

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### Video Transcript

A furniture store is displaying four tables. The lengths of the tables are five feet, 5.202 feet, 5.2 feet, and 5.26 feet. Arrange the tables’ lengths in descending order.

To write our numbers in descending order means that from left to right, we order our numbers from largest to smallest. So here we have our numbers listed just as they were given to us: five, 5.202, 5.2, and 5.26. So we need to compare these numbers. That way we can list them in descending order.

So they all are at least equal to five. The first number is exactly five, but the other three have numbers after the decimal point. So let’s go and add a decimal point to our first number. Let’s go and add a decimal point to five. Technically, five is the same as 5.0, because when working to the right of the decimal point after all the numbers that are already written, it’s okay to add zeros to the end.

So since 5.202 has three numbers after the decimal point, so in order to compare these numbers, let’s go ahead and make sure that each number has three numbers to the right of the decimal point. And like we said, it’s okay to add zeros to the end. So our first number will be 5.000. Our second number is 5.202. Our third number is 5.200. And then our last number is 5.260.

So let’s go ahead and make sure every number has three numbers to the right of the decimal point. The first one has one, two, three. The second one has one, two, three. The third one has one, two, three. And the fourth one has one, two, three. So when comparing numbers, we need to begin all the way to the left.

To the left of the decimal point, all of these numbers have five. So now, let’s compare the numbers after the decimal point because now we made sure that they all have three. So looking at the first number to the right of the decimal point, the first number has a zero, the second one has a two, the third one has a two, and the fourth one has a two, making the five the smallest, because that is the smallest number after the decimal point right now.

So now to compare the other three, we need to look to the right. We have zero, zero, and six, so six is the largest. So this must be the largest number. Now to compare the two middle numbers, we have two and we have zero, so two is larger. So 5.202 would be larger and 5.200 would be smaller.

So to write this in descending order, we have the largest to the smallest left to right. Now one other thing to look at, since we made all of the numbers have three numbers to the right of the decimal place, we could have just compared these as entire numbers, so zero, 202, 200, 260. 260 would be the largest, then we would have 202, then 200, and then lastly zero.

And it’s only okay to compare these decimals like this because they all have a value of five added to it. Therefore, the lengths of the tables arranged in descending order would be 5.26 feet, 5.202 feet, 5.2 feet, and five feet.