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

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
I would say, is a fairly straightforward example. Let’s start with
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

  • January 1, 2018 at 2:23 am
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    IM IN 6TH AND I GET THI$🐴🐘🐴🐒🐘🐨🐼🐴🐼🐒🐼🐴🐍🐴

    Reply
  • January 2, 2018 at 9:47 am
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    wow after watching this i can do the conversion with ease tysm …u made my day

    Reply
  • January 7, 2018 at 6:25 am
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    This guy sounds unsure smh

    Reply
  • January 10, 2018 at 2:16 am
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    Ayee

    Reply
  • January 13, 2018 at 5:40 am
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    this is amazing that you this is the best you teach betterbthan my teachers

    Reply
  • January 14, 2018 at 6:42 am
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    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!!!! 😀

    Reply
  • January 16, 2018 at 7:24 pm
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    I'm the only one watching in 2018 o.o what has the world become

    Reply
  • February 5, 2018 at 9:38 pm
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    I understand now

    Reply
  • February 21, 2018 at 4:26 pm
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    You study from calculator

    Reply
  • February 21, 2018 at 8:58 pm
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    THANKS THIS IS SO EASY NOW😁😁😁😊

    Reply
  • February 23, 2018 at 6:01 pm
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    LOL

    Reply
  • February 25, 2018 at 3:42 am
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    This was super helpful refresher

    Reply
  • February 27, 2018 at 10:45 pm
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    This is weird what if I have a question this is weird then what do I do

    Reply
  • March 8, 2018 at 1:31 pm
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    You explain this stuff better than my math teachers

    Reply
  • March 9, 2018 at 12:59 pm
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    Are you mad this is wrong because of you I got bad marks in my exam

    Reply
  • March 26, 2018 at 6:27 am
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    Thanks cool

    Reply
  • March 26, 2018 at 9:04 am
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    I swear I learn more here than school

    Reply
  • April 10, 2018 at 2:07 am
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    YO IM IN 6TH GRADE AND THIS SAVED MY LIFE THX SO MUCH

    Reply
  • May 5, 2018 at 2:41 pm
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    this is a classic video!

    Reply
  • May 14, 2018 at 2:23 am
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    my teachers teach it much easier ya I go to harker

    Reply
  • May 19, 2018 at 7:26 pm
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    You're my boy!

    Reply
  • May 21, 2018 at 3:32 pm
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    93 does not go into 26 two times lol

    Reply
  • May 25, 2018 at 12:15 am
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    So bottom decided by top

    Reply
  • May 25, 2018 at 12:16 am
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    this is soooooo easy now

    Reply
  • May 30, 2018 at 10:09 pm
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    Easy very easy!

    Reply
  • June 1, 2018 at 9:55 am
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    ThIs iS thE tEnThS PlaCeeee

    Reply
  • June 7, 2018 at 1:50 am
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    thank you!!!!!!

    Reply
  • June 7, 2018 at 7:42 pm
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    Isn't is 0.5?? Srry I'm Spanish sos

    Reply
  • July 1, 2018 at 2:28 am
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    Why are you saying 170 minus 93. 1.70 isn't one seventy

    Reply
  • July 10, 2018 at 1:05 pm
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    Whos watching in 218

    Reply
  • July 25, 2018 at 10:03 am
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    i love you bro.

    Reply
  • August 6, 2018 at 7:43 pm
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    Thanks really nice video

    Reply
  • August 27, 2018 at 6:16 am
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    This is way too confusing

    Reply
  • August 29, 2018 at 4:41 am
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    This helped me wi th nothing

    Reply
  • August 30, 2018 at 12:03 am
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    maths is cool to learn

    Reply
  • September 9, 2018 at 7:45 pm
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    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??

    Reply
  • September 23, 2018 at 12:10 am
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    where do you get the 2 from

    Reply
  • September 25, 2018 at 12:47 am
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    uploaded 11 years ago

    Reply
  • September 28, 2018 at 10:55 am
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    Omg tysm i have a benchmark and i forgot how to do this

    Reply
  • October 3, 2018 at 7:24 pm
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    Like how you explain stuff

    Reply
  • October 3, 2018 at 7:29 pm
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    Love how you explain stuff

    Reply
  • October 12, 2018 at 8:54 pm
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    What about the unit's place?

    Reply
  • October 17, 2018 at 12:06 am
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    You forgot to add the notation bar

    Reply
  • October 18, 2018 at 3:54 pm
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    thanks

    Reply
  • October 30, 2018 at 1:12 am
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    Teacher way: 🤔
    This vid: 😃

    Reply
  • October 31, 2018 at 7:31 pm
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    2018?

    Reply
  • November 2, 2018 at 2:50 am
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    Thx this helped me alot😀

    Reply
  • November 13, 2018 at 2:05 am
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    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

    Reply
  • November 20, 2018 at 11:17 pm
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    OMG I WASNT EVEN ALIVE AT THIS TIME…it’s crazy 😜

    Reply
  • November 21, 2018 at 1:10 pm
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    Thanks for helping me write my exam

    Reply
  • November 28, 2018 at 9:02 pm
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    Thak god youre o youtube

    Reply
  • December 3, 2018 at 3:20 am
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    2+2=5

    Reply
  • December 8, 2018 at 7:14 am
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    11 years later

    Reply
  • December 11, 2018 at 1:58 am
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    This will help my math grades tnx

    Reply
  • December 19, 2018 at 12:24 am
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    i get it but im still confused. I tried to make my fraction, 6/8 into a decimal but i got confused

    Reply
  • January 3, 2019 at 11:41 pm
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    First comment in 5 years :ppppp

    Reply
  • January 8, 2019 at 2:01 am
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    My mom made me watch this.

    Reply
  • January 11, 2019 at 6:10 am
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    This is really easy and helpful but why does the person sound like Drake?

    Reply
  • January 25, 2019 at 12:56 am
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    Thank you btw I'm in 2019

    Reply
  • January 27, 2019 at 1:11 am
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    so helpfull

    Reply
  • March 9, 2019 at 2:14 pm
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    so much easier

    Reply
  • March 10, 2019 at 12:04 pm
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    Super

    Reply
  • March 10, 2019 at 11:29 pm
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    I'm 20 and this still is annoying and confusing to me

    Reply
  • March 17, 2019 at 3:49 pm
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    Math is still boring and hard. BOOOOORING

    Reply
  • March 20, 2019 at 7:49 pm
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    It is great for kids in 6th grade

    Reply
  • March 24, 2019 at 6:37 pm
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    Can’t you just say zero point five

    Reply
  • March 27, 2019 at 2:54 pm
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    Thank you so much I’m literally subscribing you explain a lot better than anyone else

    Reply
  • April 9, 2019 at 4:34 am
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    this vid…was made before I was born… only by a couple days but still

    Reply
  • April 29, 2019 at 11:59 pm
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    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

    Reply
  • May 21, 2019 at 8:16 pm
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    But 2 divided by 1 is 2 O-O

    Reply
  • May 28, 2019 at 2:40 pm
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    thanks for your help

    Reply
  • May 29, 2019 at 10:37 pm
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    I wish you were my teacher cause this makes sense.

    Reply
  • July 2, 2019 at 4:22 pm
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    tysm! this was way easier to understand than my school

    Reply
  • July 2, 2019 at 10:17 pm
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    Thank you as always Mr. Khan. These resources are a life saver.

    Reply
  • August 15, 2019 at 9:34 am
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    2019 ?

    Reply
  • August 22, 2019 at 5:01 am
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    What's with your camera quality

    Reply
  • August 29, 2019 at 2:39 am
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    U should play fortnite and teach them maths 😂

    Reply
  • August 30, 2019 at 5:46 pm
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    My teachers never explained this….no wonder I did bad in math.

    Reply
  • September 5, 2019 at 9:37 pm
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    Wow this video was made when I was born!

    Reply
  • September 6, 2019 at 3:55 pm
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    why do teachers always make it more complicated than it needs to be so this helped a lot.

    Reply
  • September 17, 2019 at 3:28 pm
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    you so well i will recomand you to my theacher

    Reply
  • September 18, 2019 at 1:46 pm
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    i like this it helps!

    Reply
  • September 18, 2019 at 3:07 pm
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    good vid

    Reply
  • September 22, 2019 at 8:20 pm
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    Thanks

    Reply
  • September 24, 2019 at 1:43 am
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    This was made a day before my mother went in labor and gave birth to me 😍😍😍😍😍

    Reply
  • September 25, 2019 at 3:56 am
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    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😂

    Reply
  • September 27, 2019 at 12:49 am
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    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 🙂

    Reply
  • September 30, 2019 at 3:26 pm
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    2019 anyone? no its me only, k

    Reply
  • October 4, 2019 at 10:41 am
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    Thanks

    Reply
  • October 10, 2019 at 1:17 am
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    Thank youuuuuu can you just be my teacher

    Reply
  • October 10, 2019 at 10:52 pm
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    on some of my paper I am getting you divided the top to the bottom number instead the way doing for the correct answer

    Reply
  • October 18, 2019 at 6:24 am
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    ah yes, this video was uploaded 12 days after I was born.

    Reply
  • October 24, 2019 at 2:46 am
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    thanks again a lot

    Reply
  • October 27, 2019 at 9:47 am
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    Thankss you totalllyyy teach better than my teachers

    Reply
  • October 29, 2019 at 7:10 pm
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    Khan Academy taught me more in ten minutes than my math teacher did in a year

    Reply
  • October 31, 2019 at 3:02 am
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    How do you know how much zeros you need?

    Reply
  • November 5, 2019 at 1:55 pm
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    Are you from pakistan

    Reply
  • November 7, 2019 at 1:30 pm
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    Thank you for teach me how to do it you should be teacher

    Reply
  • November 12, 2019 at 11:36 pm
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    thx

    Reply
  • November 13, 2019 at 12:18 am
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    I don’t understand this method or way because my teacher 👩‍🏫 teached us another way ?????👩🏽‍⚖️

    Reply

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