We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
234
2
avatar+210 

Express \(0.\overline{1}\) + \(0.\overline{01}\) + \(0.\overline{0001}\) as a common fraction.

 Jun 14, 2018
 #1
avatar
0

Take the reciprocal of each:

0.11111111111 =1/9

0.01010101010 =1/99

0.000100010001 =1/9999

1/9 + 1/99 + 1/9999 =1213/9999

 Jun 14, 2018
edited by Guest  Jun 14, 2018
 #2
avatar+117 
0

x = 0.11111111...
10x = 1.11111111...
10x-x = 1.1111111111...-0.111111111...
9x=1
x=1/9

y = 0.0101010101...
100y = 1.0101010101010...
100y-y = 1.01010101010...-0.01010101010101...
99y = 1
y = 1/99

z = 0.0001000100010001...
10000z = 1.000100010001...
10000z-z = 1.000100010001...-0.000100010001...
9999z = 1
z = 1/9999

\(x+y+z\\ \frac{1}{9}+\frac{1}{99}+\frac{1}{9999}\\ \frac{1111}{9999}+\frac{101}{9999}+\frac{1}{9999}\\ \frac{1213}{9999} \)

 

 Jun 14, 2018

12 Online Users

avatar
avatar