Comparing decimals example

So we have four numbers listed here. What I would like you to do is get out some pencil and paper and pause this video. See if you can order these numbers from least to greatest. So the least would be at the left and then keep going greater and greater until you get to the greatest number.

So pause the video and have a go with that.

All right, now let's tackle this together. The way that I like to do it is I start at the, I guess you could say the most significant place value or the largest place value, compare the numbers, and then keep moving to the right to smaller and smaller place values.

So we can start in the ones place. This number has zero ones, this number has zero ones, this number has zero ones, and that number has zero ones. So the ones place really doesn't help us much. But then we can move to the tenths place. This number has seven tenths, this number has zero tenths, so just from that we know that the second number is less than the first number.

This has seven tenths, this has a zero tenths. It doesn't matter what's happening in the places after that to the right of that. This number over here also has seven tenths, just like the first number, and this last number also has seven tenths. So we know from comparing the ones and then the tenths place is that this number right over here is the smallest of the four numbers. They all have zero ones, but this one also has zero tenths.

So I'll list that here: zero point zero seven four. Now let's move to the hundredths place. This number has zero hundredths; we've already used this number. This number has seven hundredths, and then this number, it might not be obvious, but the hundredths place you can view as being a zero. The hundredths place, you could just put a zero there and not change the value, so this also has zero hundredths.

So these three numbers—same ones, same tenths—but this number, zero point seven seven, has seven hundredths while the other two had zero hundredths. So this is going to be the largest of our four numbers. This is larger than these other two because of what we see in the hundredths place. It doesn't matter what's happening in the thousandths place or anything beyond that, so we put the zero point seven seven right there.

Now we are tasked—and we've used this number—and now we have to compare these two numbers which were equal in the ones, tenths, and hundredths place. So we have to go to the thousandths place. This number has seven thousandths; this number has zero thousandths, so this number is smaller than this first number here.

So I'll write this next: zero point seven and then the third smallest or the next largest number is this one over here: zero point seven zero seven. And we're done.

So the main idea is you want to compare the most significant place values, the largest place values first, and then based on that keep moving to the right to compare less and less significant place values.