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.

Ayee

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

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!!!! 😀

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

I understand now

You study from calculator

THANKS THIS IS SO EASY NOW😁😁😁😊

LOL

This was super helpful refresher

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

You explain this stuff better than my math teachers

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

Thanks cool

I swear I learn more here than school

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

this is a classic video!

my teachers teach it much easier ya I go to harker

You're my boy!

93 does not go into 26 two times lol

So bottom decided by top

this is soooooo easy now

Easy very easy!

ThIs iS thE tEnThS PlaCeeee

thank you!!!!!!

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

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

Whos watching in 218

i love you bro.

Thanks really nice video

This is way too confusing

This helped me wi th nothing

maths is cool to learn

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??

where do you get the 2 from

uploaded 11 years agoOmg tysm i have a benchmark and i forgot how to do this

Like how you explain stuff

Love how you explain stuff

What about the unit's place?

You forgot to add the notation bar

thanks

Teacher way: 🤔

This vid: 😃

2018?

Thx this helped me alot😀

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

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

Thanks for helping me write my exam

Thak god youre o youtube

2+2=5

11 years later

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

First comment in 5 years :ppppp

My mom made me watch this.

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

Thank you btw I'm in 2019

so helpfull

so much easier

Super

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

Math is still boring and hard. BOOOOORING

It is great for kids in 6th grade

Can’t you just say zero point five

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

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

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

But 2 divided by 1 is 2 O-O

thanks for your help

I wish you were my teacher cause this makes sense.

tysm! this was way easier to understand than my school

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

2019 ?

What's with your camera quality

U should play fortnite and teach them maths 😂

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

Wow this video was made when I was born!

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

you so well i will recomand you to my theacher

i like this it helps!

good vid

Thanks

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

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😂

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

Thanks

Thank youuuuuu can you just be my teacher

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

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

thanks again a lot

Thankss you totalllyyy teach better than my teachers

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

How do you know how much zeros you need?

Are you from pakistan

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

thx

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

This is very helpful thanks

i approve this message

That is very hard. My teacher explains it in such a easy way using maths wise.