Master Recurring Decimals Conversion with My Advanced Math Tips

[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

book answer
31/90 38/90

 

[sjb-2812]

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?

 

[HallsofIvy]

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

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.

x=34/90 x=57/90
x=17/45 x=19/30

book answer
31/90 38/90

 

[unihopes92]

thanks for the help! XD