# Need help recuuring decimals

1. Feb 3, 2010

### unihopes92

need help!! recuuring decimals

hey, I'm in yr 11 advanced maths and I'm on a section in my book, where I'm converting recurring decimals to common fractions. i have a series of questions, after i finished the first couple i cheeked the back of the book to make sure I did them correctly but the book says they are all wrong. hears what i did and the books answer after it. p.s. the last digit is the only recurring decimal eg 4 out of .34...

.34...... .57......
x=.34...... x=.57.....
10x=3.4..... 10x=5.7.......
100x=34.4..... 100x=57.7.......
100x-10x=34 90x=57
x=34/90 x=57/90
x=17/45 x=19/30

31/90 38/90

Last edited by a moderator: Feb 3, 2010
2. Feb 3, 2010

### sjb-2812

Re: need help!! recuuring decimals

For instance, in the first case, if x = 0.344444(etc); 10x = 3.44444(etc); 100x = 34.444444(etc) , so what does 34.444444(etc) - 3.44444(etc) equal?

3. Feb 3, 2010

### HallsofIvy

Staff Emeritus
Re: need help!! recuuring decimals

No, it should be 100x 10x= 34.4...-3.4.... so 90x= 31, not 34.

Similarly, subtracting 10x= 5.7.... from 100x= 57.7.... gives 90x= 57.7.... - 5.7... or 90x= 52, not 57.

4. Feb 4, 2010

### unihopes92

Re: need help!! recuuring decimals

thanks for the help! XD