How do yout turn .15151515151515151515... into a fraction?

Question

Please help!!! I need to know how to do it!!! Not what the answer is!!!! Thanks !!!!!!!!!!!!!!!!!!

Answer 1

1/.15151515151515

Answer 2

Repeating Decimals
If the decimal is a repeating decimal instead of a terminating one, we can still convert it to a fraction. Let's try to figure out the fractional equivalent of 0.5757575757... .

Let F be this fraction. We see that the repeating group has length 2. This tells us to multiply F by 102 = 100. See what happens when we do:

F = 0.5757575757...
100 F = 57.5757575757....

Now we can subtract the first equation from the second, and the repeating part of the decimal is cancelled:
99 F = 57.0000000000... = 57

(Now you can see why we chose 102 as a multiplier. It was just to make this cancellation happen.) Now it is easy to find F. Remember to reduce it to lowest terms when you have it in the form of a fraction:
F = 57/99 = 19/33.

Sure enough, when we do long division, we find that 19/33 = 0.5757575757... .
As another example, let's convert F = 1.3481481481481... to a fraction. Since the repeating group has length 3, we should multiply F by 103 = 1000.

F = 1.3481481481481...
1000 F = 1348.1481481481481...
999 F = 1346.8000000000000...
= 1346.8 = 6734/5,
F = 6734/(5*999) = 6734/4995 = 182/135

Answer 3

If the decimal representation of a fraction terminates, then we can give the decimal fraction an exact name, using base 10 place values: .103 = 103 thousandths = 103/1000
.48932 = 48932 hundred thousandths = 48932/100000
.15 = 15 hundredths = 15/100 = 3/20
If the common fraction can't be written as an equivalent fraction with
a denominator which is a power of 10, then the decimal form of the fraction will not terminate. So the only common fractions which have decimal representations which terminate are those whose denominators contain prime factors of only 5 and/or 2 (the prime factors of the base, 10).So your fraction 355/113 will not terminate. If you think about the long division process, and about the fact that the division never terminates, then the only possible remainders at each step are 1 through 112. Since we can have at most 112 different remainders in the long division process, we must get a repeated remainder after at most 112 steps; and so the repeating decimal part of 355/113 can be at most 112 digits long.And in fact, with a large prime denominator like 113, it is quite likely that the repeating decimal pattern will be 112 digits long.One way to find the repeating decimal part is long division, as you have attempted. 3.1415929203,The next digit should be "5"; you show "4".now go to the link in the source bar
to finish ,thanks!

Answer 4

The way I convert a repeating decimal into a fraction is like this:

x=0.1515151515...
100x = 15.15151515...

(I multiplied by 100, because there are two digits that are repeating. If you'd asked me to conver .123123123... into a fraction I would have multiplied by 1000.)

Then take the difference between those two equations:

99x = 15

x = 15/99 reduce that by dividing by 3/3 to get x = 5/33

Answer 5

When you have an infinitely repeating fraction, you take the part that repeats, see how many digits are in that, and divide it by a number with the same number of digits, but all digits are 9.

That is to say...

.123123123... = 123/999. (Simplify from there.)

In this case, it's 15/99. That reduces to 5/33.

Answer 6

get a scientific calculator, put in .15151515151515151515 or whatever and push the equal button. It should turn into a fraction.

Answer 7

15151515151515151515 OVER 1

Answer 8

Call it "x"
x=0.151515151515......

then
100x = 15.1515151515......
100x - x = 15
99x = 15
x=15/99=5/33

You can apply this method to any repeating fraction.
(Although 0.999999..... is interesting)

Answer 9

1 / .15151515151515151515 = 6.6

1/6.6

Move decimal places to get whole numbers

10/66

Therefore the fraction is ten sixty sixths

Answer 10

its 15/99 savvy?