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.

Main content

Fraction to decimal with rounding

Sal writes 16/21 as a rounded decimal. Created by Sal Khan.

Want to join the conversation?

  • blobby green style avatar for user Michael Zufelt
    what does he mean at
    (77 votes)
    Default Khan Academy avatar avatar for user
    • duskpin sapling style avatar for user diva.shah
      I know this wuestion was asked 10 years ago but i understand others may be confused as well so i’ll try my best to answer this.

      Sal is saying to divide 16 by 21. Now this is because the denominator is greater than the numerator so to find the decimal, we divide 16 by 21. An easy way to remeber this is because when the numerator is greator than the denominator, it will always be 0.something. That’s how we find the decimal version.

      I hope this was helpful have a great day everyone!
      (5 votes)
  • starky sapling style avatar for user PeterParker4life
    could you do this with negative numbers? like:

    -45
    -------
    -9
    (16 votes)
    Default Khan Academy avatar avatar for user
  • mr pants teal style avatar for user Imogen
    Is there a quicker and more efficent way of doing this instead of going through the whole process of long division ?
    (10 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Joaquin Dorantes
    Why does he decide to round to the nearest ten thousandths, is there some sort of rule to use when dividing and deciding what to round to?
    (13 votes)
    Default Khan Academy avatar avatar for user
  • male robot donald style avatar for user ヤンディ™
    ⠀⠀⠀^_^⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠛⠛⠛⠛⠛⠿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⣠⡾⠟⠛⠛⠛⠿⣦⣄⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⢙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀
    ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⢱⡀⠀⠀⠀⠀⡜⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀
    ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢰⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀
    ⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇⠀⠀⠀⢸⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀
    ⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀
    ⠀⠀⠀⠹⣷⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀
    ⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⣶⣶⣶⣦⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀
    ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀
    ⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀
    ⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀
    ⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣴⡿⠁⠀
    ⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡛⠛⠉⠀⠀⠀
    ⠀⠀⠀⢀⣴⣿⠋⠁⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠈⠙⠻⣶⣄⠀⠀⠀
    ⠀⢀⣴⣿⣯⣴⡆⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢰⣶⣬⣻⣷⡀⠀
    ⠀⣾⠏⢸⣿⠿⠃⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠈⠻⢿⡿⠹⣿⡀
    ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣤⣀⣀⠀⢀⣀⣠⣤⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
    ⠀⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣿⠟⠛⠻⣿⣯⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠃
    ⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠛⠛⠋
    (12 votes)
    Default Khan Academy avatar avatar for user
  • scuttlebug green style avatar for user moritaka87
    how does he calculate that fast?
    (6 votes)
    Default Khan Academy avatar avatar for user
  • female robot ada style avatar for user Bushman Rhyane
    what is this?? How do you do this??
    (7 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user brooker9
      you can divide the top number by the bottom number or you can do what he is doing. its I little confusing for me tho because I learned this all in french but I have a good understanding of this but if the bottom number is bigger then the top number then you know the answer will be less then 1 because it cant make exactly or over one so there will be a 0. before your answer.
      (5 votes)
  • winston baby style avatar for user CalebG
    i saw a raccoon at a tree
    (7 votes)
    Default Khan Academy avatar avatar for user
  • starky ultimate style avatar for user yuling
    yo this video is pi minutes long (3.14)
    (7 votes)
    Default Khan Academy avatar avatar for user
  • spunky sam blue style avatar for user 💎Chυcκ Lørrε💎
    How many zeros did I need to add? and why sometimes just add three zeros? sometimes add five zeros?
    (6 votes)
    Default Khan Academy avatar avatar for user
    • leaf red style avatar for user Icedlatte
      You can add as many as you like, or as many as you need when you're dividing past the decimal place.
      3 zeros tend to be handy, it depends on how accurate you want the result to be

      So if you want an accurate result, say 45.2836709239......... You'll want a lot of zeros. But usually you don't need a result that accurate, so maybe just use three zeros, unless otherwise told to. Most of the time they just want you to round to 2 zeros. For example 45.28
      (2 votes)

Video transcript

Let's see if we can express 16/21 as a decimal. Or we could call this 16 twenty-firsts. This is also 16 divided by 21. So we can literally just divide 21 into 16. And because 21 is larger than 16, we're going to get something less than 1. So let's just literally divide 21 into 16. And we're going to have something less than 1. So let's add some decimal places here. We're going to round to the nearest thousandths in case our digits keep going on, and on, and on. And let's start dividing. 21 goes into 1 zero times. 21 goes into 16 zero times. 21 goes into 160-- well, 20 would go into 160 eight times. So let's try 7. Let's see if 7 is the right thing. So 7 times 1 is 7. 7 times 2 is 14. And then when we subtract it, we should get a remainder less than 21. If we pick the largest number here where, if I multiply it by 21, I get close to 160 without going over. And so if we subtract, we do get 13. So that worked. 13 is less than 21. And you could just subtract it. I did it in my head right there. But you could regroup. You could say this is a 10. And then this would be a 5. 10 minus 7 is 3. 5 minus 4 is 1. 1 minus 1 is 0. Now let's bring down a 0. 21 goes into 130. So let's see. Would 6 work? It looks like 6 would work. 6 times 21 is 126. So that looks like it works. So let's put a 6 there. 6 times 1 is 6. 6 times 2 is 120. There's a little bit of an art to this. All right, now let's subtract. And once again, we can regroup. This would be a 10. We've taken 10 from essentially this 30. So now this becomes a 2. 10 minus 6 is 4. 2 minus 2 is 0. 1 minus 1 is 0. Now let's bring down another 0. 21 goes into 40, well, almost two times, but not quite, so only one time. 1 times 21 is 21. And now let's subtract. This is a 10. This becomes a 3. 10 minus 1 is 9. 3 minus 2 is 1. And we're going have to get this digit. Because we want to round to the nearest thousandth. So if this is 5 or over, we're going round up. If this is less than 5, we're going to round down. So let's bring another 0 down here. And 21 goes into 190. Let's see, I think 9 will work. Let's try 9. 9 times 1 is 9. 9 times 2 is 18. When you subtract, 190 minus 189 is 1. And we could keep going on, and on, and on. But we already have enough digits to round to the nearest thousandth. This digit right over here is greater than or equal to 5. So we will round up in the thousandths place. So if we round to the nearest thousandths, we can say that this is 0.76. And then this is where we're going around up-- 762.