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Comparing decimals (tenths and hundredths)

Sal compares decimals like 0.7 and 0.09 with greater and less than symbols.

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Video transcript

- Let's compare the number 0.7 to the number 0.09. And there's a bunch of ways to do this, but the way that I'm going to tackle it is I'm gonna start looking at each of the digits, starting with the leftmost digit. And so we can start right over here in the ones place. You always want to compare ones place to ones place, so for example if we compare these two numbers, they both have zero ones. So the ones place doesn't tell us much. So now let's go one place value to the right. Let's go to the tenths place. This number has seven tenths, while this number has zero tenths. That by itself tells us that this is the larger number. We would put an inequality symbol right over here. We wanna open it up to the larger number, where it points to the smaller number. So this says 0.7 is greater than 0.09. Now you might be tempted to say oh wait, wait. Look, but if we went one more digit to the right you have nine hundredths here, and you have no hundredths over here. We could write a zero over here, and you'd say well look, you have no hundredths over here. But the nine hundredths don't matter. Remember, even if you had 10 hundredths, that's the same thing as one tenth. So it doesn't matter that nine is somehow greater than seven. What matters is it's in a place to the right. Even if you increased by another hundredth here you'd only get to one tenth. This thing over here has seven tenths. Let's do another one of these. Let's say we wanted to compare, let's say we wanted to compare 0.29, let's say I wanna compare that to 0.31. Now this one you might say is a little bit more straightforward, depending on how you think about it. If you say hey, this is 29 hundredths, this is 31 hundredths, we have more hundredths on the right-hand side. So let me open my inequality to the larger value and I would say 0.29, or 29 hundredths is less than 31 hundredths. Another way you could have done this is you could have looked in the ones place, say okay, they both have zero ones, but then you look in the tenths place, say this only has two tenths, while this has three tenths. I shouldn't have to keep looking at the digits to the right of that. I can just compare this two tenths to the three tenths. Three tenths is larger, and so I would say that 29 hundredths is less than 31 hundredths. Let's do one more, just for fun. Let's compare, let's compare 0.6 to, I'll do them in the same color. 0.06. Which of these is the larger number? Well we do the same thing that we've been doing. You can first go to the ones place. Say okay, this has no ones, this has no ones. Okay that doesn't tell us much. Then the tenths place. This has six tenths, this has zero tenths. So this number is going to be larger. It has more tenths. It doesn't matter who has more hundredths. Hundredths are much smaller than tenths. They're a tenth of the size of a tenth. So this has six tenths, this has zero tenths. So this number is larger. 0.6 is greater than 0.06. It's actually ten times greater but we can talk about that in other videos.