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

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

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

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.

Answer 2

Iliana was part of a group that was working on changing 0.4 repeated to a fraction. The answer is 2.25.

How to convert percent to fraction and decimal?

Percentage counts the number compared to 100.

So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:

For each 1, there are a/100 parts.

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.

Let x be 0.444444$\bar 4$

So,

4 / 10 = 0.4

4 / 9 = 0.4444444...

9/ 4 = 2.25

Learn more about fraction addition here:

https://brainly.com/question/17544795

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