How do you change 0.244444444 into a fraction?

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Answer 1 · 2015-11-06T17:56:03

This is the technique also for dealing more difficult ones. You have to decide what to multiply by guided by the repeat cycle.

Let $x = 0.244444....$ ..............(1)

so $10x = 2.44444$ .....(2)

(2) - (1)

$10x -x=2.2$
$9x =2 2/10$

$x= 2/9 + 2/90$

$x = (20+2)/90$

$x=22/90$

$x=11/45$

Answer 2 · 2015-11-06T22:41:46

Convert into a terminating continued fraction, then simplify to find

$0.2dot(4) = 11/45$

$0.2dot(4)$ is less than $1$ so the continued fraction starts $0 + 1/...$

Calculate $1/(0.2dot(4)) = 4.dot(0)dot(9)$

So our continued fraction looks like $0+1/(4+1/...)$

Subtract $4$ then calculate $1/(0.dot(0)dot(9)) = 11$

So our fraction terminates here in the form: $0+1/(4+1/11)$

$0+1/(4+1/11) = 1/(44/11+1/11) = 1/(45/11) = 11/45$