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
convert the decimal to a fraction or vice versa, and then proceed as the form dictates
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.
why do we need math? cause we dont really need it,we only need it because the world invented things and u need math for the new things to make stuff fit and work.
Just like playing an instrument or speaking a different language, knowing math gives us a new perspective on how we relate to the world around us. Even if math isn't immediately practical, the way our brains are wired with math changes how we apply ourselves. I've found that I can use the concepts learned in math to explain things such as social issues, and even silly things like how I understand music. It may not be the best answer, but I hope this helps you! :)
can anybody please tell me how to simplify a fraction please. :-)
Well, to simplify a fraction first you have to make sure none of the numbers are prime. Prime means that the number can't be divided by anything to get an integer (whole number). If the number in the numerator or denominator is prime then the fraction is simplified. If the numbers are not prime then you should find the greatest common factor. That means you have to find the largest number that both the numerator and denominator can be divided by.

If there is no number that both the numerator and denominator can be divided by then the fraction is already simplified. Please note that both numbers being divisible by 1 does not mean that you can simplify the fraction. Any number divided by 1 is itself. If your fraction can be simplified then divide both numbers by that number. If you can find another common number that both the numerator and denominator can be divided by then simplify. This shouldn't happen if you find the greatest common factor. Although sometimes using lower numbers is easier. Keep simplifying and checking to see if any of your numbers are prime or do not have a common factor.

At this point your fraction is simplified. :) Feel free to reply if you have any questions. Sorry for the bad paragraph formatting, the reply started out as a big blob of text.
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.
Probably because math is a series of number and variables in most cases, nothing special about math really. Just takes pratice and lots of doing, never a way to study... Just try to remember the formulas and form it is written in. Also, keep working out the equations, try to view examples online, and sooner or later it will seem to get easier or less complicated
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.
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)
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!
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%.
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
I don't get it how he got 2 3/4? Someone explain please! i understand the other concepts but i need help !
After doing a lot of fraction exercises, I got into the habit of trying to "simplify" a fraction *every* single time -- because a simple fraction is easier to read. For example, "two and three fourths" (2 3/4) is easier for me to say and think about than "two and seventy-five one-hundredths" (2 75/100). Not all fractions simplify, but if you CAN simplify a fraction, it's usually good to do so -- but HOW did Sal know that 2 3/4 is just another name for 2 75/100?
(in other words, that there are just as many 3s in 75 as there are 4s in 100.)
Well, he probably noticed that 75 ends with a "5" and that 100 ends with a "0" (any number that ends with a zero is a multiple of 10 -- and ten is just two 5s) so he must have suspected that there was definitely a number he could divide both by.
If you start with 5, and divide both numbers by that, you'll get "2 15/20". But if you notice, 15 ends with a "5" just like 75, and 20 ends with a "0" just like 100 -- so we know the numbers are still not as simple as they *could* be. Let's divide them both by five again, and now we have "2 3/4". Since "3" is a "prime" number, we know the fraction won't simplify any more.
Since we used 5 twice, we know the shorter way would be to just divide 75 and 100 both by 25 in one step (since 5x5=25). And that's why Sal used 25.
Here's a video Sal did, if you want to watch more about breaking large numbers into smaller ones:
Isn't 2 3/4 a mixed number instead of a simplified fraction? Shouldn't the answer be 11/4?
Well... yes, you're onto something there. Although decimal form, mixed number form and improper fraction form are all compatible forms to express the same quantity and all three forms are equivalent. But in reality, for a number to be considered as a fraction, it should be written in the fraction form, improper or otherwise.

So yes, I would say you're right about this one. The task was to write it as an improper simplified fraction. Sal should have converted the mixed number into an improper fraction. But the important thing is that you understand the concept.
If i were to add fractions to a decimal then multiply it by a negative number what would i do
You would want to reduce as far as possible and then Solve. Do you know what an improper fraction is?
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.
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
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!
I have a question... when you make 7/10 into a common 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
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
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
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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
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?
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?
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.
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.
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?
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.
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
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.
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
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?