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What is 5.228 (with the 8 repeating) as a fraction?

 Feb 24, 2022
 #1
avatar+114 
0

1741/333 = 576/333

 Feb 24, 2022
 #2
avatar+124595 
+2

We don't need to worry about the "5"  part, yet

 

1)  Take 228  and subtract  the non-repeating part of the decimal  =  228- 22 = 206....this is our numerator

 

2) In the denominator, write the same number  of 9's as the repeating part  of the decimal= 9

    And write the same  number of 0's as the non-repeating part  of the decimal = 00

 

So  .228 (8 repeating)  =   206 / 900 =   103 / 450

 

So we have

 

5 + 103 / 450   =  2343 / 450

 

cool cool cool

 Feb 24, 2022
 #3
avatar+36433 
+2

Here is another method :

 

x   = 5.228

100x = 522.8888.....

1000x = 5228.8888.....

 

1000x - 100x =  900x =   5228.8888....   - 522.8888....    = 4706

900x = 4706

x = 4706/900   simplify as needed                     (=  5  103/450) 

 Feb 24, 2022
 #4
avatar+124595 
+1

Thks, EP......I never remember this method, but it's a good one....!!!

 

 

cool cool cool

CPhill  Feb 24, 2022

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