fraction equivalent of 0.888888?

8/9

most of the above are right when you mean 0.88888....

if you mean exactly 0.888888 it is
888888/1000000 = 222222/250000 =
111111/125000 =
11*10101 / (5*5*5*1000)
11*13*7*111/(5*5*5*40*25)
11*13*7*3*37/(5*5*5*(2*2*5*2)*(5*5)

no more factors in common
so 0.888888 = 111111/125000

The answer is 8/9. Below is the proof.

Let's set n = 0.888888888...

Multiply both sides by 10:

10n = 8.8888888...

Subtract the original equation from the second, cencelling out the repeating eights:

10n = 8.88888
n = 0.88888
============
9n = 8

solve for n

n = 8/9


Want an interesting excercise, do the same thing to figure out the fraction equivalent to 0.9999999999 :)

0.888888 = 88.8888/100 = 8.88888/10

Let x = 0.888888

First move the decimal point to the right, so that the first "block" of repeated digits appears before the decimal point. Remember that multiplying by 10 moves the decimal point 1 position to the right.

So move the decimal point 1 position to the right, by multiplying BOTH sides by 10:

Therefore 10x = 8.88888

Now subtract the original number, x, from both sides, to get rid of everything after the decimal point.

10x - x = 8.88888 - x
9x = 8.88888 - 0.888888 = 7.999992 = 8.
x = 8/9

I hope that helped! Feel free to email me for more questions.

me07. :-)

8/9

Check out the link or google for "converting recurring decimals into fractions"

http://www.google.com/search?q=converting+recurring+decimals+into+fractions&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

Cheers,

Kempos

8/9

0.xxxxx = x/9
0.xyxyxy = xy/99
0.xyzxyz = xyz/999

and so on

4/5 ?