# Question Video: Comparing Two Decimal Numbers Mathematics • 4th Grade

Complete using <, =, or >: 5 tenths ＿ 70 hundredths.

03:23

### Video Transcript

Complete using the symbol for is less than, is equal to, or is greater than. Five-tenths what seventy hundredths.

In this question, we’ve got two values that we need to compare together. And there are a combination of both digits and words. We’ve got five-tenths and then there’s seventy hundredths. Now a very easy mistake to make here would be just to look at the numerals and say to ourselves, “Well, I know that five is a lot less than 70, so five-tenths must be less than seventy hundredths.” Now, in a moment we’re going to compare these values, and it might be the case that the first one is less than the second, but it’s not because five is less than 70. And that’s because these values are talking about two different place value units. We’ve got five-tenths and seventy hundredths.

Let’s sketch a couple of models to help us see what these values actually mean. We could represent five-tenths by taking a whole square splitting it into 10 equal parts and then shading five of them. There are no whole squares, but there are five-tenths of a square. So we’d write this value as 0.5 if we were writing it in digits. Our second value is a number of hundredths. Now, just like all the other columns, the hundredths place can only fit one digit in. But we’re told that this value is worth seventy hundredths. If we were to sketch this as a model again, we’d need our whole square and, this time, to split it into 100 equal parts. Then we’d need to shade in 70 of them.

So once again, we’ve shaded in zero whole squares and we’d write seventy hundredths with a seven in the tenths place and a zero in the hundredths place. If we drew another model, can you see that seventy hundredths is actually the same as seven-tenths? That’s why that digit seven goes in the tenths place. Now we’ve sketched these two models; we can compare the values quite easily. We can see that five-tenths is less than seventy hundredths. As we’ve just seen, seventy hundredths is the same as seven-tenths. And we know that five-tenths must be less than seven-tenths.

Another way we could find the same answer is by looking at our place value table and comparing the digits. Both numbers have zero ones, but our first number has five-tenths and our second number has seven-tenths. So it turns out that five-tenths is less than seventy hundredths. But it’s not because five is less than 70. To find the answer, we needed to work out what five-tenths and also seventy-hundredths were worth. And we use both models and also a place value table to help compare them. Five-tenths is less than seventy hundredths. And so the symbol that we need to use in between these two values to compare them is the one that represents less than.

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