Question

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Answer 1

Answer:

Let us say that 0.6666… =x

Multiplying both sides with 10,

10x=6.66666…

Subtracting the two equations

We get

9x=6

Transposing 9 to the other side

X=6/9=2/3

Answer 2

Answer:

Let Consider The Fraction Of p/q Form As " x "

Let x = 0.66666.. = 0.6 Recurring - Eq.n 1

$\sf After\: Multiplying \: All \: by \: 10 \bf$

10x = 6.6666.. = 6.6 Recurring - Eq.n 2

$\sf Now \: Subract \: Eq. \: no.\: 1 \: From. \: Eq \: no. 2 \bf$

$\begin{gathered}:\implies\sf{ 10x - x = 6.66666.. - 0.66666.. }\\ \\ \\ :\implies\sf{ 9x = 6} \\ \\ \\ :\implies\sf{ x =}\dfrac{ 6}{9}\end{gathered}$

Therefore , 0.6666.. = 6/9