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Comparing decimals: 156.378 and 156.348

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

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  • aqualine ultimate style avatar for user apredator504
    So after thousandths it is ten thousandths?
    (8 votes)
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  • aqualine tree style avatar for user Nevergiveup
    Does the place value of the whole number effect it?
    (7 votes)
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  • blobby green style avatar for user James Horne
    what is bigger 3489 or 3469 can u make it in a video plss?
    (5 votes)
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    • stelly blue style avatar for user Kim Seidel
      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.
      (5 votes)
  • blobby green style avatar for user az.cummings
    ok um this is hard can somebody help me
    (5 votes)
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  • duskpin ultimate style avatar for user Matthew.Arthur.Marquez
    There the same. It's just the four and six in the hundredths place. Comparing them is now easer.
    (5 votes)
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  • aqualine seed style avatar for user Keira Allen
    Why is there no oneths place? PLEASE explain that to me
    (2 votes)
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  • piceratops ultimate style avatar for user 𝓜𝓪𝓱𝓮𝓼𝓱 𝓜𝓪𝓱𝓮𝓷𝓭𝓻𝓪𝓴𝓪𝓻
    At ,what does Sal mean by saying "because in the more significant place.."?And isn't the 8 in the thousandths place significant?
    (3 votes)
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    • piceratops ultimate style avatar for user Hecretary Bird
      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.
      (4 votes)
  • blobby green style avatar for user 347606
    Nevergiveup, yes, yes it does
    (4 votes)
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  • aqualine sapling style avatar for user Gabrielle
    ok now i feel dumb for not knowing this
    (3 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      I assume you’re asking about comparing decimals.

      First, line up the decimal points. This is an important step! If there are any missing digits, you can write 0’s for them.

      The idea is that columns to the left are more important than columns to the right. Start at the column farthest to the left and compare the digits. Larger digits in this column mean larger decimals.

      Only if there’s a tie, go to the next column to the right and compare those digits. Larger digits in that column mean larger decimals. Continue this process until there are either no more ties or no more digits.

      Have a blessed, wonderful day!
      (3 votes)
  • starky tree style avatar for user lloy
    you said the number was greater, but you didn´t explain you said this number is less than this number thsi number is greater then this decimal is greater and I dont get it
    (4 votes)
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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.