If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Comparing decimals: 156.378 and 156.348

Sal compares 2 decimals using place value. Created by Sal Khan.

Want to join the conversation?

• in the number 2,145,857 how does the digit 5 in the thousands place compare to the digit 5 in the tens place?
• Well, first of all, since the 5 in the thousands place is in a higher place value than the 5 in the tens place. Using this information, we can convert each of these 5s into numbers based on their place value, which will give us 5000 and 50. 5000 is evidently larger than 50. IT would be 100 times larger which you can figure out by dividing 5000 by 50.
• I understaned but its cofusing can you explain a littel diffrently?
• If you watch the video again, you may understand it better.
• What grade are you in? I would appreciates a lot of upvotes
• I still don't get why you would ignore the 8ths place.
• Because there is no chance the number could be bigger since the place before it is larger.
• So after thousandths it is ten thousandths?
• Yes.Tenths,hundredths,thousandths and ten thousandths.:)
• what is bigger 3489 or 3469 can u make it in a video plss?
• Since your 2 numbers have the same number of digits, compare the digits from left to right until you find a digit that is different.
For example - which is smaller: 53,892 or 53,982
-- The 1st digits are both 5
-- The 2nd digits are both 3
-- The 3rd digits are different the 1st number has 8, the other has 9. 8 is smaller than 9. So, the 1st number (53,892) is the smallest of the 2 numbers.

Now, try the process with your 2 numbers. Comment back if you have questions.
• Does the place value of the whole number effect it?
• At ,what does Sal mean by saying "because in the more significant place.."?And isn't the 8 in the thousandths place significant?
• When he says "significant place", Sal means that the place has a larger impact on the value of the number. For example, let's take 10.2.
If we change the 0.2 to maybe 0.3, the number's value only increases by 0.1. However, if we take a more significant place, such as the 10 and change it to 20, the number's value practically doubles! So, the tens place has more impact, or is more significant than the tenths place.
As you leftwards in a number, the places get more and more significant. As you go rightwards, they get more and more precise.
• ok um this is hard can somebody help me
• There the same. It's just the four and six in the hundredths place. Comparing them is now easer.

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.