Question

Iliana was part of a group that was working on changing 0.4 repeated to a fraction. Each member of the group had a different answer. Which answer is correct?

Answer 1

Answer:

C (4/9)

Step-by-step explanation:

Answer 2

$\bf 0.444444444\overline{4}\impliedby \textit{and keeps on going}\\\\ -------------------------------\\\\ \textit{let's say }\boxed{x=0.444444444\overline{4}}\quad \textit{ thus }10\cdot x=4.44444444\overline{4} \\\\\\ \textit{wait a minute! }4.44444444\overline{4}\textit{ is really just }4+0.444444444\overline{4}$

$\bf \textit{but we know }x=0.444444444\overline{4} \textit{ so then }4+0.444444444\overline{4}=\boxed{4+x} \\\\\\ \textit{wait a second! }10\cdot x\implies 10x=4.444444444\overline{4}=4+x \\\\\\ thus\qquad 10x=4+x\implies 10x-x=4\implies 9x=4\implies \boxed{x=\cfrac{4}{9}}$

you can check in your calculator.

anyhow, to get the "recurring decimal to fraction", you start by setting to some variable, "x" in this case, then move the repeating part to the left of the point by multiplying it by some power of 10, and then do the equating.