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Comparing decimals: 156.378 and 156.348

This video is all about comparing decimals. Learn how to determine which decimal is greater by comparing each place value, starting from the left and moving right, until a difference is found. Created by Sal Khan.

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Video transcript

We're asked to compare 156.378 to 156.348. So I assume that they're asking us which of these is greater. And so let's rewrite these numbers. 156.378, and we want to compare that to 156.348. And it might already be obvious to you which of these is greater. But I'll work through it step-by-step, just in case it's not. So let's first go to the hundreds place. And you could view this as, to some degree, the most significant place, because this is where they have the largest-- the 1 in the hundreds place represents a lot more than a 1 in the tens place or a 1 in the six's place. A 1 in the hundreds place represents 100. It's this many hundreds. But we have the same number of hundreds in both situations. We have 1 hundred and we have 1 hundred. Let's go to the tens place. We have 5 tens here, which is 50. And we have 50 right over here. So, so far they're equal, so far, if you just look at the hundreds and the tens place. Let's go the ones place. We have a 6 here in the ones place, 6 ones, which is really just 6. And you also have 6 ones. So, so far, they're equal again. Let's go to the tenths place-- 3 tenths, 3 tenths. Let's go to the hundredths place. So we're going into smaller and smaller places. So then you have the 7 hundredths. And now we have 4 hundredths here. So this has less hundredths than this does over here. And if we go to the thousandths place, these are equal. But it doesn't matter, even if these were unequal. It doesn't matter, even if this one was larger than this one, because in the more significant place, this number was larger than this number. So 7 is greater than 4. We have 7 hundredths here. We have 4 hundredths here. So we get this number is greater than this number down here. Or 156.378 is greater than 156.348. And in particular, it's because of the hundredths place.