Question

The question says express each repeating decimal as a fraction:

5.23232323

This is my work but my answer doesn't seem right:

100x= 523.23232323
- 10x= 52.23232323
90x= 470.909090
/ 90x. \90x
x= 5.23232323

What am I doing wrong?
And how am I suppose to know when to multiply x by 10,100, or 1000?
Thank you!!

Answer 1

every repeating decimal of n digits, say, abc can be written as

abc/999

where the denominator of n digits is 10^9-1

So, .<u>23</u> = 23/99
5.<u>23</u> = 5 23/99 = 518/99

You should have written

100x = 523.23...
x = 5.23...
99x = 518
x = 518/99

If there are n repeating digits, multiply by 10^n