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What common fraction (that is, a fraction reduced to its lowest terms) is equivalent to \(.3\overline{25}\) ?

tertre  Dec 23, 2017
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5+0 Answers

 #1
avatar+80973 
+1

For this one

 

1)  Ignore the decimal

2)  Take the "whole" and subtract the non-repeating part  =  325 -  3   =  322

3) Put this over a number that has the same number of 9's as the repeating part  =  99, followed by the same number of 0's as the non-repeating part  = 0

 

4)  So we have

 

322  / 990  =   161  / 495

 

Verify for yourself that this is equal to the required decimal

 

 

cool cool cool

CPhill  Dec 23, 2017
 #2
avatar+1364 
+1

thanks so much!

tertre  Dec 23, 2017
 #3
avatar+1602 
+1

I have not seen a interminably repeating decimal be converted into a simplified fraction in the fashion Cphill described above, but I will present to you an alternate method. On further review, though, the method I have below appears to prove Cphill's method.

 

\(x=0.3\overline{25}\) Firstly, I set the repeating decimal equal to a variable. I will use the standard choice, x.
\(x=0.325252525...\) A few more decimal places should be written out so that the method is clear. 
   

 

Now, multiply x by a factor of ten such that the repeating portion lines up with the first line.

 

\(10x=3.25252525...\\ \hspace{5mm}x=0.325252525...\) Notice how the repeating portion does not line up here, so this is not the correct multiple of ten. Let's multiply both sides by ten again.
\(100x=32.525252525...\\ -(\hspace{1mm}x=\hspace{2mm}0.325252525...)\) Look at this! Notice how the repeating portion of both equations line up perfectly. Now, subtract the two equations from each other.
\(99x=32.2\) Now, solve for x. 
\(x=\frac{32.2}{99}\) Apply a multiplication of 10/10 to simplify the fraction.
\(x=\frac{322}{990}=\frac{161}{495}\)  
   
TheXSquaredFactor  Dec 23, 2017
 #4
avatar+80973 
0

Thanks, X2.....!!!

 

 

cool cool cool

CPhill  Dec 23, 2017
 #5
avatar+2 
0

I appreciate it!. I really like it when people get together and share ideas. Great website, continue the good work!. Either way, great web and I look forward to seeing it grow over time. Thank you so much. |=>super smash flash 2 |=>bloons tower defense 5
 

rebeccahic  Dec 25, 2017

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