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Worked example: Converting a fraction (7/8) to a decimal

Learn how to write the fraction, 7/8 as a decimal. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • blobby green style avatar for user esthervimartin
    Video is great but how do you know what exact numbers to submit as your answer after the decimal point for the practice segment? Example 7/30 = 0.233333333... but they only took 0.233 as the answer. Could someone please clarify?
    (220 votes)
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    • leaf blue style avatar for user John
      it depends on how are you going to round it off.
      for example, the answer should be rounded off to the nearest thousandths then the answer will be 0.233
      but if it said round it of to the nearest hundredths then it will be .23
      (177 votes)
  • mr pink red style avatar for user kulkainat
    i get it but how would u do a mixed number?
    (35 votes)
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  • starky sapling style avatar for user 25.jaclyn.siar
    how do we put this into percent?
    (9 votes)
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  • blobby yellow style avatar for user SARIN V S
    What if the question was convert 0.9999999...... to a fraction. It gives the answer answer as 1. Why is it coming like this. How is that even possible.
    (7 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      Interesting question! Consider the difference 1-0.9999999...... . Clearly this difference is greater than or equal to 0, but less than every decimal in the infinite sequence 0.1, 0.01, 0.001, 0.0001, ... . The only real number that meets all the conditions in the previous sentence is 0. So, in the real number system, the difference 1-0.9999999...... is 0. Therefore 0.9999999...... equals 1 in the real number system!
      (10 votes)
  • blobby green style avatar for user Azzabk345
    how many zeros we must add to the 7
    (9 votes)
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    • duskpin ultimate style avatar for user Tanel Kagan
      You can add as many as you like to begin with, because zero is just that - nothing. It doesn't matter how many you add, it doesn't change the value.

      However, it's sensible to only add as many zeroes as you need, otherwise your working could look messy with a string of zeroes that you might not need.

      That's why the best approach, during the long division process, is to add them one at a time. Each time there is a remainder, you add another zero (you don't actually have to write it in up there, but it helps to keep everything in its correct place) and do your division then subtraction again.

      When no remainder is left, you can stop - no further zeroes are needed and you will have your answer. That is unless your answer is a repeating decimal, in which case you need to be able to recognise that else you will be calculating forever!
      (1 vote)
  • aqualine ultimate style avatar for user levi.marske
    so what if you have a number like pi over another
    (7 votes)
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    • leaf green style avatar for user Matthew Yung
      Do you mean like π/x (x is any digit)?
      Normally when we want to do it simple we just leave it like this mainly because pi is irrational and the decimal places are almost infinite.
      If you want to get an approximate answer you will need a calculator.
      (3 votes)
  • blobby green style avatar for user DIEGOF
    How can you memorize the multiplication tables?
    (4 votes)
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    • stelly blue style avatar for user Kim Seidel
      Practice, practice and more practice.
      Start by skip counting: 5, 10, 15, 20, etc.
      Then, start working on more random multiplication. Like what is 5x9?

      You don't have to do every thing at once. Start with the smaller values and work your way up. If you have a friend who also wants to memorize the tables, you can quiz each other.
      (5 votes)
  • starky seed style avatar for user pryah.816313
    can you do dividing with frations
    (3 votes)
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  • piceratops tree style avatar for user Blaine Smith
    how do you know where to put the decimal at?
    (6 votes)
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  • piceratops seed style avatar for user Vana
    Is there another method that i can use for this?
    (3 votes)
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    • blobby green style avatar for user LD
      Sometimes, then you see that multiplying denominator by some number produces power of 10, i.e. 10, 100, 1000 so on, you can multiply numerator and denominator by that number and division gets easy. Say, you want to convert 11/20. You know that 20*5=100. then: 11*5/20*5= 55/100=0.55. For proper fractions, you can simply write multiplied numerator after "0."
      (5 votes)

Video transcript

Write 7/8 as a decimal. And so the main realization here is that 7/8 is the same thing as 7 divided by 8, which is the same thing as 7 divided by 8. These are all different ways of writing the same thing. So let's actually divide 8 into 7. And I'll do it down here just so I have some more real estate to work with. I'm going to divide 8 into 7. And I'm going to add a decimal point here, just because we know that this value is going to be less than 1. 7/8 is less than 1. We're going to have some digits to the right of the decimal point. And let me put the decimal point right up here, right above the decimal point in 7. And then we start dividing. And now this really turns into a long division problem. And we just have to make sure we keep track of the decimal sign. So 8 goes into-- it doesn't go into 7 at all, but it does go into 70. So 8 goes into 70 eight times. So it goes into 70 eight times. 8 times 8 is 64. And then you subtract. 70 minus 64 is 6. And then bring down another 0 because we still have a remainder. We want to get to the point that we have no remainders. Assuming that this thing doesn't repeat forever. And there's other ways we can deal with that. 8 goes into 60? Well, let's see. It doesn't go into it eight times because that's 64. 8 goes into 60 seven times. 7 times 8 is 56. And then we subtract again. 60 minus 56 is 4. And now, we can bring down another 0 right over here. And 8 goes into 40? Well, it goes into 40 exactly five times. 5 times 8 is 40. And we have nothing. We have nothing left over. And so we're done. 7 divided by 8 or 7/8 is equal to 7 divided by 8, which is equal to 0.875. But I'll put a leading 0 here just so it makes it clear that this is where the decimal is. 0.875. And we are done.