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avatar+1222 

2.01333=> generating fraction

 Jul 11, 2015

Best Answer 

 #1
avatar+33614 
+10

Do you mean the 3's to go on forever?  If so, then try 604/300

 

$${\frac{{\mathtt{604}}}{{\mathtt{300}}}} = {\frac{{\mathtt{151}}}{{\mathtt{75}}}} = {\mathtt{2.013\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

.

 Jul 11, 2015
 #1
avatar+33614 
+10
Best Answer

Do you mean the 3's to go on forever?  If so, then try 604/300

 

$${\frac{{\mathtt{604}}}{{\mathtt{300}}}} = {\frac{{\mathtt{151}}}{{\mathtt{75}}}} = {\mathtt{2.013\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

.

Alan Jul 11, 2015
 #2
avatar+14538 
+8

Good morning Dbg4thebest and Alan !

x = 2.01333...         10 x =  20.13333...

10x - x = 9 x             20.13333... - 2.01333 = 18.12

9x = 18.12       =>   900x = 1812    =>      x = 1812 : 900 = 1812 / 900

 

  x= $${\frac{{\mathtt{1\,812}}}{{\mathtt{900}}}} = {\frac{{\mathtt{151}}}{{\mathtt{75}}}} = {\mathtt{2.013\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

 

 

 $${\frac{{\mathtt{1\,812}}}{{\mathtt{900}}}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{151}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{75}}\right)}} = {\frac{{\mathtt{151}}}{{\mathtt{75}}}}$$

 

Gruß radix !

 Jul 11, 2015

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