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

 

[CellCoree]

Hi there! I'm glad to hear that you are working on converting recurring decimals to common fractions in advanced math. This is a very important concept and will definitely come in handy in more advanced math topics.

From what you have shown, it seems like you have the right idea but there may be a mistake in your calculations. Let's take a closer look at the first problem (.34...):

You correctly multiplied both sides by 10 to eliminate the recurring decimal. However, when you subtracted 10x from 100x, you should have gotten 90x instead of 100x. This is because 100x - 10x is equal to 90x, not 100x.

So the correct calculation would be:
100x - 10x = 34
90x = 34
x = 34/90
x = 17/45

As for the second problem (.57...), the same mistake was made. The correct calculation would be:
100x - 10x = 57
90x = 57
x = 57/90
x = 19/30

I hope this helps you understand where the discrepancy lies and how to correctly solve these types of problems. Keep practicing and you'll master converting recurring decimals in no time! Good luck with your studies.