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Decimal to simplified fraction

Here's an example of how we convert a decimal to a simplified fraction. Over time this will become second nature to you.

Decimal to simplified fraction

Discussion and questions for this video
how do you convert a fraction into a decimal?
You should divide fraction's numerator by denominator.

For example:
3/4 = 3 : 4 = 0,75

Sal made few videos about it, here is one:
Can any body help me with the first question of converting decimals to fractions 1?

i have to convert 0.22 into a fraction.

Please answer quickly.
First, you count the number of numbers(numerals greater than 1)on the _right_ side of the decimal place,(in your case, 2)than, you move the decimal place right that many times(in your case to get 22)than divide that number by one with that many zeros on it's right side(100) with 22 over it so 22/100. Than simplify to get 11/50.
How do I write a mixed number as a percent
how do you change a decimal to a fraction when it has 3 numbers behind the decimal?
Hey Olivia!

When changing a decimal to a fraction when it has 3 numbers behind the decimal, you may try to do the following:

Suppose that your decimal is 1.234. You may want to associate it with a fraction involving someone associated to the "family of tens". Who could divide 1234 (the whole number without decimals) in order to bring the decimal so far?
Since we have three decimals, the answer would be someone in the family of tens with three zeros - Which is the number 1000, getting us to the fraction 1234/1000 - Leaving us with the simple job to simplify it.

If you think of the number 123.4, the process is the same: Just think about who in the family of tens would bring the decimal that far. Since there is 1 decimal value, we would think about someone in the family of tens with a single zero: 10 itself! The fraction would be 1234/10 in this case.
How do you add Decimals and fractions?
convert the decimal to a fraction or vice versa, and then proceed as the form dictates
so when i make a mixed number to improper fraction iin dividing fractons i have to flip it around again?
I don't think so. 1 3/4 will turn into 7/4.
how can you make a vidio?
Use your camera and maybe post it on YouTube. If you want the same software as Mr. Khan, I'm not sure what it's called, but you could check on the KA Discussion Forum.
The answer would be 0.14, or 7/50, since .126 can be written as 63/500, then if you cross multiply it with 11.9, you get 7/50.
If 46% = 30 sheets of paper, how do I find out how many sheets = 54%
This will be a two step problem.
The first step, you will need to figure out the total number of sheets of paper. Put the 46% over 100% and the 30 sheets of paper over X, and set them equal to each other.

46/100= 30/X
Cross multiply and you get
Next divide 3000 by 46 to get the total sheets of paper.
X=65.22 sheets of paper.
Now, you have to figure out 54% of that. Simply multiply .56 by 65.22.
The answer is 36.5232 or ~36 sheets of paper
How would I go about approximating .68 inch to the nearest eighth of an inch?
First you would need to find which 8ths it falls between.
4/8 = 0.5
5/8 = 0.625
6/8 = 0.75
So we will be rounding to either 5/8 or 6/8 and need to decide which one is closer.
.68 - .625 = .055
.75 - .68 = 0.07
0.055 < 0.07 so we round to 5/8.

The other way to do it would be to first multiply 0.68 * 8 to get 5.44. This rounds down to 5 then divide by 8 so again we get 5/8.
What is a mixed number? I forgot. :/
A mixed number is a whole number, such as 3, -3, or -1, connected to a fraction. An example of a mixed number is 3 1/2.

I hope this helps!
isn’t 2.75 = 275/100?
Yes, 2.75 = 275/100, but we can simplify that. It simplifies into 2 75/100 which simplifies down again to 2 3/4.
How do i write a fraction as a percent if the numerator is not divisible by the denominator (e.g. 5/7)?
5/7 = 0.7142857143 and so on
*100 = 71.42857143
you would have to round it as you wish. that's why it's better kept as a fraction for accuracy.
how do you convert 22/32 into decimals
You have to divide 22 by 32.
the area of a square Is 144ft square . what is the length of one of the sides of the square?
To find the length of the side of a square, you find the *square root* of the total area. In this case, the length would be *12 ft*, since the square root of *144* is *12*.
i just don't get how you can change a decimal into a fraction it has been confusing me for a while so do you think anyone could help me understand it better?
decimals into fractions: use the place value of the decimal number
.75 means 75 hundredths, so write it 75/100, then reduce (divide) 75 and 100 both by 25, to get 3/4. (75/25=3, 100/25=4)
how to convert a percent(%) as an improper fraction
To convert a percent to an improper fraction, you need a percent with a value that is greater than 100 percent. Let's say that you had a percent such as 134%. You can convert this percent into 1 34/100 because you have one whole 100% and 34% left over.

I hope this helps!
Hi How do you convert a fraction to a decimal i dont really get it
That is actually very simple to do. Let me give you an example:
What is the decimal form of 1/2?
All you do is treat the bar as a division bar and voila!
So 1/2 would be 1 divided by 2, which is 0.5.
HELP!! How do you do percent times percent? It is so confusing...
it's just like regular multiplication, but you have to convert the percents to decimals first and remember the rules about how multiplying decimals work. so 50% time 60% is .5 times .6 which equals .3. convert that back into a percent, you get 30%.
I was a little lost but after watching the video again i got it
Er, today at my school, my teacher asked what was 0.23 in fraction and no one knew it, please help so i tell my teacher.
You should first say the name of the decimal number. Since the final digit is in the hundredths place, you would call it twenty-three hundredths. There is a fraction with the same name.
if you have a fraction that is like lets say 25/100 it is going to be 25 percent
it is 1/4 in fraction.
Why do we have decimals and fractions and percents?
Why don't we just have one like fractions and not have any other?
There are many contexts in which numbers are used. Each type of number is ideal at times when others are not. We have variety to maintain flexibility.
Hey sal i am in 7th grade and these videos r awesome, iwas wondering how you would simplify o.oo32
it would be:

how do you convert a decimal into a percentage?
@kayliels it would mean:

.54 = 54%

2.89 = 289%

.0095 = .95%
so you can just add the fraction by making a picture.
yes. it will help u visualise it
can you make more examples?
okay so lets say we had 10/20 to make it smaller halve it once you will automatticly have 5/10 but if you had 60/70 you would have to halve it a couple of times! that was the fractions! if we had 10/50 just take the dit away and add the decimal point its that easy! that was the decimal!
Can this way be used for all problems like that?
I have a question... when you make 7/10 into a common denominator...do you just add a zero to the end to make it the same?
well i need a lot of help on decimals and fractions,can you help me please?
what your are i dont no but i same answering you the its very simple decimals friction only convrt into point from thaky you
can you help me with decimals and fractions i am kinda having some troubles with that kind of stuff thank you!
decimails are very simple because the friction from convort into point from OK!
i have very difficutl promble in rationalnumber
can you help me?
how do you simplify 9 7/8
you make it into a mixed number then start dividing by the common divisor
how to add decimals and fractions
ok if you have 2/3 + 1/7 it might be 3/10 LEAVE ME ALONE SPARKLEZ
Hey guys, I just figured out an amazing shortcut to converting decimals to fractions. If you already know how to read decimals, it should be easy. By that, I don't mean, (four point three two one). I mean, (four and three hundred twenty-one thousandths). If you don't know how to read decimals, check out this link:
Okay, back on topic. An easy way is to just read the decimal out loud, then write down the fraction just like it sounds. Here's an example:

Write 4.93 as a simplified fraction.
First, read it out loud to yourself.
_Four and ninety-three hundredths._
Now, write it down just like you read it.
4 93
Last but not least, simplify the fraction if necessary.

Pretty cool shortcut, huh?
how do you convert say 27/7 ( < thats a fraction/ mixed number ) into an improper fraction?
27 / 7 is an improper fraction. If you wanted to convert 27 / 7 to a mixed number, you would divide 27 by 7. In which case, you would have 3 and 6 / 7
Isn't it easier to just divide the numerator with the denominator, to convert to decimals?
Instead of having 2 (in 2.75) as a mixed number is there a way for it to be a fraction like 275/1000
How do you solve application problems that involve quadratic equations
are there easier ways too understand this concept for people dealing with special needs??
Try talking with your teacher about it. Maybe stay afterschool for a little bit and discuss the video. If you're homeschooled, talk with your parents or discuss it with a friend. Hope this helps! :D
who tells us all this info,i wonder
if you have 8/16 what goes into 8 that also goes into 16-2 so how many times does it go into it and you have your anser (1/2)
i hope i explained it clearly
any body out there that know how to get black hole badges

answer soon
I think I know someone who has the Telsa badge.He told some people how to get all six black hole badges.
Telsa (get 10 million energy points) Atlas ( achieve mastery in 600 unique skills)
Hypatia (achieve mastery in 350 unique skills, now a sun badge) Be Sal (be salmon Khan) artemis ( we don't know yet) gissanndo (watch all the videos Khan posted)
How do I covert mixed number to decimals. Like....19 1/2
For this question I would first convert the fraction part to a decimal. 1/2 = 0.5 You can do 1.0 ÷ 2 by long division to get this. Then add the whole number part. 19 + 0.5 = 19.5
does the first number of the decimal always stay the same when u are turning it to a mixed number
The denominator stays the same unless simplifiable.
So at around 1:58 he says "they have common factors" what does he mean by that exactly?
he had 75/100 , so in this case 25 is a factor of both numbers. ie 75 = 25 x 3 and 100 =25X4

in general factors of a number are numbers that can be used to build up that number , ultimately you get to prime factors where the number cant be broken down any more. There are videos on this topic if you didn't manage to get to them.
What happens if there is a thousandth? For example: 8.452? How would you write that as a fraction?
It would be 8 452/1000. Then you just have to reduce the fraction.
What if you have something like 6/51 how would you convert that into a decimal? I'm just not understanding the process I guess. I've read the other comments and tried at school, but I can't get it in my head. I'm finishing 8th grade if that matters.
Hi Jake. Finishing 8th grade is very important. This means you need a quick, easy way of understanding how to convert fractions to decimals. Decimal are going to be very important in Algebra I and II.
So here is a quick and easy way to find the decimal: construct a division problem. Take the numerator (6, in this case) and put it inside the division sign.
) 6*

Good? now put a decimal point after the whole number. So it should look like this:
) 6.*

Now put the denominator (51) on the outside:

51) 6.

Okay? Now put the decimal directly above, in the product area.

* -----.
51) 6.*

Now complete the problem. You should have one number in front of the decimal point (because 6 is only one digit) and the rest should be behind the decimal point.

The answer will be 0.1176470588 (etc.) Round it and you'll get approximately 0.118.

Hope this helps. If you need more help, just say so and I can give a lot more examples.
how come I just lost all my achievements for watching videos?!?
Is it just me or did it happen to anyone else?
what makes you arrived at three all over four?
75 / 100 = (3 x 25) / (4 x 25) Since 25/25 = 1, (25 is GCF of 75 and 100), 75 out of 100 is the same as 3 out of 4.
Is there an easy way to figure out how to simplify 5754/10,000?
First, look at the 2 numbers. You have 5754 and 10,000. You'd have to figure out what the GCF of both numbers are.. or just see.. 2 goes into both numbers, so divide them both by 2, and so on and so on.
whats the answer to 7 over 26
How do you change a fraction into a decimal and vise versa?
Well, you start out by finding out how many numbers are behind the decimal.
17 has 2 numbers. So if it had 1 number (lets call it ?) then it would be ?/10, but since there are 2 numbers it is 17/100. Since 17/100 isn't divisible by anything the answer is 17/100!
I need to turn 1/6 to a decimal. The answer is supposed to be .1666, I don't understand how they got the 1?
Hey Nicole!
Not sure how you are getting that answer... The easiest way to do it is to plug it into a calculator but if you go ahead and divide it out you should get the same answer. How were you doing the problem?
how do you order fractions
first you convert them into decimals.Next or der the decimals from lesat to greatest then convert them back into a fraction. A good smart-thinking tip always label what each fraction equals to the decimal. for example 1/4=0.25 thats a good tip so its less work. :)
Can anyone explain how to do the cut and copy excersies I dont understand them at all.. for example this question..

The starting block below is 116 units long. Use the tools to the right to convert the starting block into both of the goal blocks that are 23 units long and 56 units long. You can see your progress as the current blocks.

Cutting the starting block into x pieces is the same as dividing it by x.

We want to cut the starting block into a piece that can be copied into both goal block 1 and goal block 2.

The least common denominator of 3 and 6 (the denominators of the goal blocks) is 6. Therefore you can copy a block 16 units long to make both goal blocks.

To find the number of slices to cut the starting block into we solve for s in the following equation:





We now have a resulting block that is 16 units long. Now we simply divide our goal blocks by this value to see how many times we need to copy the resulting block.



I really dont get this explanation at all.
how do you convert an infinite decimal into a fraction
If the decimal does not have a repeating pattern, then the number is irrational and cannot be converted into a fraction.
However, if there is a pattern, then the way I do it is to write the repeating pattern in the numerator, then count up the digits in the numerator and write that number of nines in the denominator then simplify.
.102102102... = 102 / 999 = 34 / 333
Why cant i just write 75/100 in the first place because .75 is just 75/100
How do you convert a fraction into a decimal
Identity and place the following numbers into three groups --- less than 1/4; between 1/4 & 3/4; more than 3/4
(a) 0.4 (b) 0.76

Rosalyn 🌺
Hey Rosalyn!
Idk if the other guy already answered your question or not, but I thought I would go ahead and post an answer here in case it can help you or someone else.
1/4 is equal to 0.25, and 3/4 is equal to 0.75, so 0.4 would be greater than 1/4 (or 0.25) and also between 1/4 (0.25) and 3/4 (0.75).
0.76 is greater than 3/4 or 0.75.
I'll also write it out a different way just so you can see it. Here is the first number, 0.4.
1/4 < 0.4 < 3/4
The second number, 0.76:
1/4 < 3/4 < .76

Hope this helped and didn't just make things more confusing. :) let me know if I can help clarify anything.
"2:01" So we're supposed to find the largest number that fits into both?
Oh! I get it. Thanks!
how do you find out how to divide decimals?
The only way I remember is turn them into fractions and do this:

a/b divided by c/d. Invert c and d and change it multiplication.

a/b multiplied by d/c. Multiply numerator and denominator. Then change back to decimals.

Hope this helped! :D
How do you get a black hole badge
They are near-impossible. Good luck!
wat if its was like there was giomg on and on do we have to put a infinity bar yes or noo like we leave it like that?
How do it from the fraction to the decimal not from decimal to fraction
If it is a fraction, e.g. 2/5, try to make the denominator into multiples of 10 (10,100,1000) so for 2/5 it becomes 4/10 then take the numerator and move the decimal point to the left once for each 0 after the 1 ( if 10 then once, if 100 then twice etc..) so in this case move it once. Therefore 2/5 = .4
can you please go slower ????
hey mvegareagan by the way what a rude thing to say you are a meen person dont talk to me that way why dont you stop being lazy find a girl friend {like you even have one}and get a life
What if it's an odd number? Or a number that just can't divide evenly? Then do we split the decimal into more? Does that make it more complicated? And what if a beginner encounters it?
were can i answer the problem at.
I am sorry I don't know what you mean. Khan
I dont understand how to take a decimal and turn it into a fraction and then simplify it.. Please help me!!!
so you would just move the decimal place over? and put it over the place value?
How do u convert fractions with division
First, if the fractions are mixed, you must changed them into improper fractions. If they are just regular fractions, then all you have to do is flip the second fraction.
4/5 divided by 5/4
4/5 stays the same, but 5/4 is changed to 4/5

After you flip it, all you have to do now is multiply them as if nothing ever happened, just multiply the fractions. Then, there's your answer, but don't forget to simplify.
cant you just put 2.75 into 75/100 and simplipy it isnt it way easier than adding 7/10 and 5/100 because 75 is more than 10 and 5 is in the 100's place and it takes lesser time well that is how i got tought.and for 75/100 an easier way is thinking that 75 is 3 quarters and 100 a dollar equal to 4 quarters
no that is not what i meant i meant to say that you leave the 2 how it was and add it.........
and then you have 2 3/4
How do I convert a decimal as a fraction or mixed number
A bit hard to explain, but I'll try.
.9 would equal 9/10 because .9 is pronounced as "nine TENTHS"

.123 would be 123/1000 because the last number is in the THOUSANDTHS place.
Do you see the relationship?

TIP: Don't forget to reduce the fraction if needed!
I didn't get this until now.But now I am stuck on doing the second one.
Can this appear on the CST's?
how do you simplify
You simplify by using the LCM for example 4/8 is 2/4 or 1/2 because I can divide 4 and 8 by both 2 and four but it has to be same divisor for both like 12/24 is 1/2 if you divide both by two and 1/2 half cant be simplified make sure you can't simplify anymore before answering or it will be wrong. :-)
how did he get the answer i don;t under stand this can some one help
Are you even watching the video?
o i get it now he explains it a lot better
this is hard but i think i can do it
converting a mixed number is hard with a decimal number
What is the reciprocal of 2/3?
yes, 3/2 is the exact reciprocal of 2/3.
Thanks. This really helped me understand
I am still a little stuck on this. Can someone help!
How would you simplify a fraction like this 2/6
Numbers: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ...
The highest number that goes into 2 and 6 is 2
What is 1/8 as a decimal and a percent?
how do you covert improper fractions to decimals?
you can convert the fraction to a mixed number, and then convert the mixed number into a decimal
how do I convert fractions to percents
Well, look it:


(1/2)*100 = 1*X >> x = 50%

so, you will multiply the fraction by a hundred percent, see another sample:


(2/3)*100 = 1*x >> 200/3 = x >> x = 66,6%
what about 5 .54 i do not get that
How do you turn .38 to a fraction
what times 45 equals 24,000?
Easy, divide 24000 by 45.
how do you convert 0.0735 to a fraction huh I really need to know
do you think Sal rocks
SAL WAY ROCKS. He's like the god of math or something! :)