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Margaret [11]
2 years ago
11

Write the recurring decimal 0.2 as a fraction in its simplest form.

Mathematics
2 answers:
kompoz [17]2 years ago
8 0

Answer:

0.\.{2}=\dfrac{2}{9}

Step-by-step explanation:

Let x equal the recurring decimal:

x=0.\.{2}=0.2222\dots

Multiply both sides by 10:

\implies 10x=2.222\dots

Eliminate the recurring part of the decimal by subtracting the equation of x from the equation of 10x:

\begin{array}{ l r c l}& 10x & = & 2.222...\\\\- & x & = & 0.2222...\\\\\cline{1-4}\\& 9x & = & 2\end{array}

Divide both sides by 9:

\implies x=\dfrac{2}{9}

BabaBlast [244]2 years ago
5 0

Answer:

\sf \bold{\dfrac{2}{9}} }

Explanation:

Recurring decimal means the number keeps repeating.

0.2 is the recurring digit

x = 0.2222...

10x = 2.2222...

10x -x = 2

9x = 2

x = 2/9

0.222... ≈ 2/9

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