SOLUTION: rind the fraction form for the repeating decimal 0.4444

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Question 71318This question is from textbook advanced algebra
: rind the fraction form for the repeating decimal 0.4444 This question is from textbook advanced algebra

Answer by sudhir(14) About Me  (Show Source):
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Let y = .444444444(and so on)
so, 10y = 4.4444444(and so on)
so, 10y - y = 4.444444(and so on) - .4444444(and so on)
Now as we assume that 4 is repeating after the decimal place indefinitely so we can easily approximate the decimal parts of 4.44444444 & .44444444 to be equal so ,
10y - y = 4
9y = 4
y = 4/9 Answer.