Can you help me change repeating decimal to fraction!?

Not obvious, I had to look this up!

First say x=0.2717171...

to get the 71 lined up after multiplication, multiply by 100

100x=27.1717171...

Subtract x to get

99x=26.9

Multiply by 10 to get
990x=269, so x=269/990.

So number 2

x=0.12345345345...
Multiply by 1000 to get the 345 lined up ready to subtract
1000x=123.45345345...

Subtract
999x=123.33
x=123.33/999 = 12333/99900
Cancel by 3
x=4111/33300

And number 3

x=2.7812121212
100x=278.121212
Subtract
99x=275.34
x=275.34/99 = 27534/9900 =9176/3300 = 4588/1650
=2294/825

Or if you just want the answers, use http://www.easycalculation.com/recursive-fraction.php

1)
x = 0.2717171717171...

100x = 27.17171717171...
100x - x = 27.17171717171... - 0.2717171717171...
99x = 26.9
x = 26.9/99
x = 269/990

= = = = = = = =

2)
x = 0.12345345345345345...

1000x = 123.45345345345345...
1000x - x = 123.45345345345345345... - 0.12345345345345345...
999x = 123.33
x = 123.33/999
x = 12333/99900
x = 4111/33300

= = = = = = = =

3)
x = 2.78121212121212121212...

100x = 278.121212121212...
100x - x = 278.12121212121212... - 2.781212121212121212...
99x = 275.34
x = 275.34/99
x = 275.34/9900
x = 27534/9900
x = 4589/1650

Let's assume x=0.171717...
Then 100x = 17.171717...
100x-x=17 =>
99x=17 =>
x= 17/99;
So 0.00171717.. = x/100 = 17/9900;
0.27171717.. = 17/9900 + 27/100 = 269/990.

In the same way we can obtain the next results:
0.12345345345345345.... = 4111/33300;
2.781212121212121212.... = 4589/1650.

0.27171717171...
= 0.2 + 0.0717171....

0.2 = 1/5

x = 0.0717171....
100x = 7.171717...
100x = 7.1 + x
99x = 71/10
x = 71/990

0.27171717171...
= 1/5 + 71/990
= 198/990 + 71/990
= 269/990

----------------------

0.12345345345.....
= 0.12 + 0.00345345345....

0.12 = 12/100

x = 0.00345345345....
1000x = 3.45345345....
1000x = 3.45 + 0.00345345...
1000x = 3.45 + x
999x = 345/100
x = 345/99900

0.12345345345.....
= 12/100 + 345/99900
= 11988/99900 + 345/99900
= 12333/99900
= 4111/33300

-------------------------------

You can do the other question in the same way
2.7812121212....
= 2 1289/1650
= 4589/1650

umm I'm fairly sure this is right

You move the decimal point 2 spaces to the right. then you have twenty seven one hundreths or 27/100 because the decimal point is in the hundreths place.umm then you simplify.
you do that for all of them. If you need more help ask =]