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Express \(0.5\overline{10}\) as a common fraction.

 Jul 22, 2020
 #1
avatar+30929 
+1

Let  x = 0.51010101010....

10x = 5.1010101010....

1000x = 510.1010101010....

 

1000x - 10 x = 505

990x = 505

x = 505/990 = 101/198

 Jul 22, 2020
 #2
avatar+1130 
+2

we know that 0.5=1/2 and this is 0.0101010... more than 1/2 and we know that 100/199=0.502512563...,101/199=0.507537688,102/199=0.512562814... so 0.5101010... is in between 101/199 and 102/199 so we have that 0.5101010... is 101/198

 Jul 22, 2020

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