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

Guest Sep 26, 2020

edited by
Guest
Sep 26, 2020

#1**+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

power27 Sep 26, 2020

#3**0 **

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