how do you convert repeating decimals (.333333333and so on...) into fraction?

Question

I need to convert 4.4444444444444444444444444444...

Answer 1

Here is how you do it.

First, you multiply the number so that you have something in front of the decimal place, so, to get 3.33333... that means you multiplied it by 10. Then, you subtract the value from the multipled value, so that
3.33333... - 0.33333... = 3.0 (evidently)
but the first value is 10 times the original, and you just subtracted one, so the value 3.0 is (10-1) 9 times the value.
So, one time the value, 0.333... is thus 3/9.

This method will work with other repeating factor as well. Say, you have 0.2787878... Here you multiply it by 1000 to have 278.78787..., and if you subtract 10 times the value, 2.787878...
you would get 276, and that would be 1000 - 10 times the value, or 990 the original.
So 276/990 is 0.2787878...
Of course, 276/990 can be simplified, by dividing both numerator and demoninator by 3, to get 92/330, and we can then simplify by 2 to have 46/165; but that is another story.

Answer 2

the only different between 4/9, which gives you .444444444 is one decimal, so

(4/9) * 10^1 = (4/9) * 10 = (40/9), this gives you 4.444444

Some other repeating fractions are

(1/9), (2/9), (3/9) or (1/3), (4/9), (5/9), (6/9) or (2/3), (8/9)
(1/11), (2/11), (3/11), (4/11), (5/11), (6/11), (7/11), (8/11), (9/11)
also any number divided by 7, except for numbers that are divisible by 7.

There are many others, but the most common are numbers divided by 9.

Answer 3

This is a general method to convert recurring decimals to fractions. We are not doing anything to the integer part. Put it aside. Now take
x=0.44444444444444444444444....
So,
10x=4.444444444444444444
!0x-x=4 (decimal part gets cancelled!)
9x=4
or
x=4/9

You can also use the same technique to find
0.33333333..
0.595959.. etc..,

Another very useful method is to use the summation in a Geometrical progression.
0.44444444...=4/10+4/100+4/1000.....
The first term is 4/10(a) and 1/10 is the common ratio(r). Now consider this as an infinite series and find the sum using
S=a/(1-r)

Answer 4

to remodel decimals to fractions, you're taking the decimal style (ex. .3025 is going to 3025) and positioned it over a million observed with techniques from as many 0s as there are decimal places (thus 4, so the denominator is 10000). Then cut back it so a techniques as plausible.

Answer 5

4 and 4/9

Answer 6

set equal to variable
.3(reap) = a
multiply both sides by 10 (or how every many digits repeating, i.e. 100 for 45(bar over top))
3.3(reap) = 10a
subtract 1a
3 = 9a
(3.3(reap) - .3(reap) = 3)
then solve for a like normal
3/9 = a
1/3 = a
1/3 = .3(reap)
ur done!

Answer 7

.3333333333333333333333333..=1/3
4.444444444444444....=4 4/9 or 40/9

Answer 8

Yeah, Phil gave you the correct answer.

x/9 = 0.xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx....