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Convert thsi repeating decimal into a fraction:

 

0.435454545454...

 Mar 8, 2021
 #1
avatar+31212 
+1

x = .435454......

 

100x = 43.5454......

10000x = 4354.5454.....

 

10000x - 100x = 9900x = 4311

                                 x = 4311/9900 = 479/1100

 Mar 8, 2021
 #2
avatar+498 
-1

since 0.54545454... is just \(\frac{6}{11}\)

we then know that 0.00545454... is \(\frac{6}{1100}\) and 0.43 is just \(\frac{43}{100}\),

0.43545454... = \(\frac{(43)(\frac{1100}{10})}{1100}+\frac{6}{1100} = \frac{473 + 6}{1100} = \frac{479}{1100}\)

 Mar 8, 2021

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