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Find the fraction that equals 0.7766666666... (repeating 6's)

 Jan 31, 2022
 #1
avatar+23183 
+2

One way to find the fraction that equals  0.77666666666...

 

Let  x  =  0.77666666666...

 

To handle the 0.77, multiply this equation by 100:  (because there are two places)

--->     100x  =  77.66666666...

 

To handle the repeating 6s, multiply this equation by 10:  (because there is one place that repeats)

--->    1000x  =  776.666666...

 

Subtract these equations:  1000x  =  776.6666666...

                                    -        100x  =    77.6666666...

To get:                                   900x  =  699

 

Solve this for x:                           x  =  699 / 900                (this can be reduced)

 Jan 31, 2022
 #2
avatar+675 
0

699/900 = 233/300

 Jan 31, 2022

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