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Ordering decimals

2m read
·Nov 11, 2024

What we're gonna do in this video is do a few examples ordering numbers that involve decimals.

So let's say that we had the numbers 1.001, 0.113, and 1.101. What I would like you to do is order these numbers from least to greatest. Take out some paper and try to do it on your own before we do it together.

All right, now let's do it together. The way I would tackle ordering numbers is I would go to the largest place value that the numbers have in common. In this situation, we have a ones place value in all of them. We could see that this has 1 one, this has 0 ones, and this one has 1 one. The thing that has the least ones is going to be the smallest of the numbers.

So this one over here is going to be the smallest of the number. So let me just write that over here: 0.113.

Now we have to figure out which one is next between 1.001 and 1.101. Well then we just go to the next place value. We go to the tenths place and we see right over here they're equal on the ones place. If you go to the tenths place, this one has 0 tenths, while this one has 1 tenth. So the number on the right here is going to be larger. It has more tenths. Same number of ones, but it has more tenths. It doesn't really matter what happens to the right of that.

So the next smallest number if we're ordering from least to greatest is going to be 1.001. Last but not least would be this one that is the largest: 1.101.

Let's do another example. Let's say we had the numbers 0.424, 0.343, and 0.443. Pause this video and try to order these from least to greatest on your own.

Once again, the idea here is always start with the largest place value and then compare, then keep moving to the right if some things are equal.

All right, now let's do this together. They all have 0 ones, so they're all equal there, so that's not going to tell us much. Now let's go to the tenths place. Here I have 4 tenths, here I have 3 tenths, and here I have 4 tenths. So I don't—you have to look at the hundredths or the thousandths place. This one has the least tenths, so I can put that as the least or the smallest of the three numbers: 0.343.

Now I've already used that one, and so I need to compare these two numbers. They have the same number of ones, they have the same number of tenths, so then we move to the hundredths. Here I have 2 hundredths, here I have 4 hundredths. This one has less hundredths than this one, so the one on the left is going to be the next smallest number.

So then we have 0.424, and then last but not least, this one right over here. It has the same number of ones as everything else, it has more tenths than this middle one, and the same number of tenths as the left one, but then it has more hundredths than the left one right over here.

So this is the largest of the numbers: 0.443. And we're done.

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