# Converting fractions to decimals | Decimals | Pre-Algebra | Khan Academy

I’ll now show you how
to convert a fraction into a decimal. And if we have time, maybe
we’ll learn how to do a decimal into a fraction. So let’s start with, what
the fraction 1/2. And I want to convert
that into a decimal. So the method I’m going to
show you will always work. What you do is you take the
denominator and you divide it into the numerator. Let’s see how that works. So we take the denominator– is
2– and we’re going to divide that into the numerator, 1. And you’re probably saying,
well, how do I divide 2 into 1? Well, if you remember from the
dividing decimals module, we can just add a decimal point
here and add some trailing 0’s. We haven’t actually changed the
value of the number, but we’re just getting some
precision here. We put the decimal point here. Does 2 go into 1? No. 2 goes into 10, so we go 2
goes into 10 five times. 5 times 2 is 10. Remainder of 0. We’re done. So 1/2 is equal to 0.5. Let’s do a slightly harder one. Let’s figure out 1/3. Well, once again, we take the
denominator, 3, and we divide it into the numerator. And I’m just going to add a
bunch of trailing 0’s here. 3 goes into– well, 3
doesn’t go into 1. 3 goes into 10 three times. 3 times 3 is 9. Let’s subtract, get a
1, bring down the 0. 3 goes into 10 three times. Actually, this decimal
point is right here. 3 times 3 is 9. Do you see a pattern here? We keep getting the same thing. As you see it’s
actually 0.3333. It goes on forever. And a way to actually represent
this, obviously you can’t write an infinite number of 3’s. Is you could just write 0.–
well, you could write 0.33 repeating, which means that
the 0.33 will go on forever. Or you can actually even
say 0.3 repeating. Although I tend to
see this more often. Maybe I’m just mistaken. But in general, this line on
top of the decimal means that this number pattern
repeats indefinitely. So 1/3 is equal to 0.33333
and it goes on forever. Another way of writing
that is 0.33 repeating. Let’s do a couple of, maybe a
little bit harder, but they all follow the same pattern. Let me pick some weird numbers. Let me actually do an
improper fraction. Let me say 17/9. So here, it’s interesting. The numerator is bigger
than the denominator. So actually we’re going to
get a number larger than 1. But let’s work it out. So we take 9 and we
divide it into 17. And let’s add some trailing 0’s
for the decimal point here. So 9 goes into 17 one time. 1 times 9 is 9. 17 minus 9 is 8. Bring down a 0. 9 goes into 80– well, we know
that 9 times 9 is 81, so it has to go into it only eight times
because it can’t go into it nine times. 8 times 9 is 72. 80 minus 72 is 8. Bring down another 0. I think we see a
pattern forming again. 9 goes into 80 eight times. 8 times 9 is 72. And clearly, I could keep
doing this forever and we’d keep getting 8’s. So we see 17 divided by 9 is
equal to 1.88 where the 0.88 actually repeats forever. Or, if we actually wanted to
round this we could say that that is also equal to 1.–
depending where we wanted to round it, what place. We could say roughly 1.89. Or we could round in
a different place. I rounded in the 100’s place. But this is actually
the exact answer. 17/9 is equal to 1.88. I actually might do a separate
module, but how would we write this as a mixed number? Well actually, I’m going
to do that in a separate. I don’t want to
confuse you for now. Let’s do a couple
more problems. Let me do a real weird one. Let me do 17/93. What does that equal
as a decimal? Well, we do the same thing. 93 goes into– I make a really
long line up here because I don’t know how many
decimal places we’ll do. And remember, it’s always the
denominator being divided into the numerator. This used to confuse me a lot
of times because you’re often dividing a larger number
into a smaller number. So 93 goes into 17 zero times. There’s a decimal. 93 goes into 170? Goes into it one time. 1 times 93 is 93. 170 minus 93 is 77. Bring down the 0. 93 goes into 770? Let’s see. It will go into it, I think,
roughly eight times. 8 times 3 is 24. 8 times 9 is 72. Plus 2 is 74. And then we subtract. 10 and 6. It’s equal to 26. Then we bring down another 0. 93 goes into 26–
about two times. 2 times 3 is 6. 18. This is 74. 0. So we could keep going. We could keep figuring
out the decimal points. You could do this indefinitely. But if you wanted to at least
get an approximation, you would say 17 goes into 93 0.– or
17/93 is equal to 0.182 and then the decimals
will keep going. And you can keep doing
it if you want. If you actually saw this on
exam they’d probably tell you to stop at some point. You know, round it to the
nearest hundredths or thousandths place. And just so you know, let’s try
to convert it the other way, from decimals to fractions. Actually, this is, I
think, you’ll find a much easier thing to do. If I were to ask you what
0.035 is as a fraction? Well, all you do is you say,
well, 0.035, we could write it this way– we could write
that’s the same thing as 03– well, I shouldn’t write 035. That’s the same
thing as 35/1,000. And you’re probably
saying, Sal, how did you know it’s 35/1000? Well because we went to 3–
this is the 10’s place. Tenths not 10’s. This is hundreths. This is the thousandths place. So we went to 3 decimals
of significance. So this is 35 thousandths. If the decimal was let’s
say, if it was 0.030. There’s a couple of ways
we could say this. Well, we could say, oh well
we got to 3– we went to the thousandths Place. So this is the same
thing as 30/1,000. or. We could have also said, well,
0.030 is the same thing as 0.03 because this 0 really
doesn’t add any value. If we have 0.03 then we’re only
going to the hundredths place. So this is the same
thing as 3/100. So let me ask you, are
these two the same? Well, yeah. Sure they are. If we divide both the numerator
and the denominator of both of these expressions by
10 we get 3/100. Let’s go back to this case. Are we done with this? Is 35/1,000– I
mean, it’s right. That is a fraction. 35/1,000. But if we wanted to simplify it
even more looks like we could divide both the numerator
and the denominator by 5. And then, just to get
it into simplest form, that equals 7/200. And if we wanted to convert
7/200 into a decimal using the technique we just did, so we
would do 200 goes into 7 and figure it out. We should get 0.035. I’ll leave that up to
you as an exercise. Hopefully now you get at least
an initial understanding of how to convert a fraction into a
decimal and maybe vice versa. And if you don’t, just do
some of the practices. And I will also try to record
another module on this or another presentation. Have fun with the exercises.

## 100 thoughts on “Converting fractions to decimals | Decimals | Pre-Algebra | Khan Academy”

1. den denology says:

Ayee

2. Smart tech gamer STG says:

this is amazing that you this is the best you teach betterbthan my teachers

3. Navster Cupcake says:

Thank you so much! This is so much easier now! I think I can pass my math class ((cause, what they where teaching me was waaaaayy less simple than this video)) anyway, thank uuuu!!!! 😀

4. GAMER King says:

I'm the only one watching in 2018 o.o what has the world become

I understand now

6. erum irfan says:

You study from calculator

7. Elon Hinton says:

THANKS THIS IS SO EASY NOW😁😁😁😊

8. karina higareda says:

LOL

9. Ray1846 says:

10. gavin thompson says:

This is weird what if I have a question this is weird then what do I do

11. Fred Waters says:

You explain this stuff better than my math teachers

12. Han llool says:

Are you mad this is wrong because of you I got bad marks in my exam

13. Bruce Dusmez says:

Thanks cool

14. Jonathan Ee says:

15. Craigggg says:

YO IM IN 6TH GRADE AND THIS SAVED MY LIFE THX SO MUCH

16. Letroid Hepburn says:

this is a classic video!

17. Sonia Yu says:

my teachers teach it much easier ya I go to harker

18. satyakiran kesanasetti says:

You're my boy!

19. Nick Drake says:

93 does not go into 26 two times lol

20. Tristan Ramnarine says:

So bottom decided by top

21. Tristan Ramnarine says:

this is soooooo easy now

22. Kiran Kamboj says:

Easy very easy!

23. Erin Chantal says:

ThIs iS thE tEnThS PlaCeeee

24. Tamim Al Thani says:

thank you!!!!!!

25. LeahZzz _ says:

Isn't is 0.5?? Srry I'm Spanish sos

26. Agent Skg says:

Why are you saying 170 minus 93. 1.70 isn't one seventy

Whos watching in 218

28. John Carter says:

i love you bro.

29. Tehmina Zafar says:

Thanks really nice video

30. Mollei Taylor Williams says:

This is way too confusing

31. itzmyday 7 says:

This helped me wi th nothing

32. Hope Aki Leituala says:

maths is cool to learn

33. anita M says:

im confused!! i learnt 35 yrs ago u add the decimal on top i dont remember adding it next to the #. is this a new way of doing it??

34. Jose Ortega says:

where do you get the 2 from

35. RopticbAsE says:

36. iixAndrea says:

Omg tysm i have a benchmark and i forgot how to do this

37. Student Valyn Reid says:

Like how you explain stuff

38. Student Valyn Reid says:

Love how you explain stuff

39. Hernan Do says:

40. Blaze 7506 says:

You forgot to add the notation bar

41. Cainan Davis says:

thanks

Teacher way: 🤔
This vid: 😃

43. BapeReborn says:

2018?

Thx this helped me alot😀

45. Friendly neighborhood Spider-Man says:

My teacher can teach it the same way but in class i'll just zone out and not understand so i just watch these videos cause i actually pay attention and understand

46. Nisreen Alsabbar says:

OMG I WASNT EVEN ALIVE AT THIS TIME…it’s crazy 😜

47. SHIVEN .flute says:

Thanks for helping me write my exam

48. Jman 26 says:

49. Elias Durgin says:

2+2=5

50. beast, omar bahaa says:

11 years later

51. Isabel Silva says:

This will help my math grades tnx

i get it but im still confused. I tried to make my fraction, 6/8 into a decimal but i got confused

53. OoOO F says:

First comment in 5 years :ppppp

My mom made me watch this.

55. Gia Benipal says:

This is really easy and helpful but why does the person sound like Drake?

56. MJ Da Beast says:

Thank you btw I'm in 2019

57. Miriam rosenedd says:

58. Lilly Kawala says:

so much easier

59. Rameshs Gowda says:

Super

60. Sara says:

I'm 20 and this still is annoying and confusing to me

61. Simplejam3 says:

Math is still boring and hard. BOOOOORING

It is great for kids in 6th grade

63. Ryan Reynolds says:

Can’t you just say zero point five

64. Isabella Blackwell says:

Thank you so much I’m literally subscribing you explain a lot better than anyone else

65. Gina Hatcher says:

this vid…was made before I was born… only by a couple days but still

66. fenicks says:

Learned how to do this in like 1 minute of watching this video. We went over this for about a month in algebra, our periods are like an hour long. I learned more in one minute here, then in over a day in public school. THANK YOU KHAN

67. Striker180x says:

But 2 divided by 1 is 2 O-O

68. Virginia Stouffer says:

69. koalaman 7007 says:

I wish you were my teacher cause this makes sense.

70. Ast0reo says:

tysm! this was way easier to understand than my school

71. T Hunter says:

Thank you as always Mr. Khan. These resources are a life saver.

72. Indianna Franz says:

2019 ?

73. Ashantha KUMARAGE says:

74. Shahid Asmi says:

U should play fortnite and teach them maths 😂

75. Pumpkin Life says:

My teachers never explained this….no wonder I did bad in math.

76. Fearless kilzombies says:

Wow this video was made when I was born!

77. Miss Bumblebee says:

why do teachers always make it more complicated than it needs to be so this helped a lot.

78. Aaron Feagin says:

you so well i will recomand you to my theacher

79. LEAH KAUFMAN says:

i like this it helps!

80. Alexander Middendorf says:

good vid

81. Jake Helms says:

Thanks

82. a doe a deer says:

This was made a day before my mother went in labor and gave birth to me 😍😍😍😍😍

83. CNC Nation says:

Lol I’ve watched abt 5 videos on this it’s 11:55 it’s a school night and I’m just hoping this knowledge will sink in my brain for tomorrow😂

84. zara soh says:

I'm trying out for a really good school, and this helped me understand a lot! The book didn't explain it has well as u did 🙂

2019 anyone? no its me only, k

86. Zarina Husain says:

Thanks

87. Daniel Chavez says:

Thank youuuuuu can you just be my teacher

88. Lisa Jules says:

on some of my paper I am getting you divided the top to the bottom number instead the way doing for the correct answer

89. its_ crazey says:

ah yes, this video was uploaded 12 days after I was born.

90. max oconnor says:

thanks again a lot

91. Rhodora Hernandez says:

Thankss you totalllyyy teach better than my teachers

92. Ugly Rat says:

Khan Academy taught me more in ten minutes than my math teacher did in a year

93. Daisy Villa says:

How do you know how much zeros you need?

94. Robert Burn says:

Are you from pakistan

95. PanPan BCISB says:

Thank you for teach me how to do it you should be teacher

96. Chris Dunn says:

thx

97. Jessica collier says:

I don’t understand this method or way because my teacher 👩‍🏫 teached us another way ?????👩🏽‍⚖️

98. Fatma Ulutas says: