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Express  \(3.\overline{444}\) as a base 10 fraction in reduced form.

 Sep 26, 2020
edited by Guest  Sep 26, 2020
 #1
avatar+234 
+1

to start, we will ignore the 3 and come back to it later

we are left with the fraction .4444444444444

i see this and reconize that it is 4/9, but if you dont there is a way we can get there algabraicly

x=.444444444

multiply by 10

10x=4.44444444444

subtract the original equation

9x=4

divide by 9, and you get x=4/9

 

coming back to the 3

4/9+3=(3(9)+4)/9

=31/9

 Sep 26, 2020
 #2
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i tried 31/9 but it says it is wrong

Guest Sep 26, 2020
 #3
avatar+234 
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put 31/9 into a calculator, it is equal to 3.444444

 

is the base 10 part supposed to mean something? i just assumed it meant that it didn't want the fraction to be in base 7 or anything.

power27  Sep 26, 2020
 #4
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Yes. They want the decimal 3.44444...  converted to base 10 as a simplified answer

Guest Sep 26, 2020
 #5
avatar+234 
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then what number base is 3.444444 supposed to be converted from

power27  Sep 26, 2020
 #6
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sorry, i meant simplified fraction

Guest Sep 26, 2020
 #10
avatar+111124 
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If it says 31/9 is wrong, then try entering it in a different way.

 Sep 26, 2020

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