Question

Evaluate: $0.\overline{6}+0.\overline{3}-0.11$.

Answer 1

Step 1: Write the decimal in fraction form.

The given expression is $0.\overline{6}+0.\overline{3}-0.11$

Let $x=0.\overline{6}$ Or $x=0.66...---\left(1\right)$

Multiply both sides by $10$ we have:

$10x=6.66....---\left(2\right)$

Subtract equation (1) from (2) we have:

$$\begin{gathered} 10x-x=6.666...-0.666.... \\ 9x=6 \\ x=\frac{2}{3}[Dividingbothsidesby9\&simplifying] \end{gathered}$$

Similarly let $y=0.\overline{3}$ or $y=0.333....----\left(3\right)$

Multiply both sides by $10$ we have:

$10x=3.33....---\left(4\right)$

Subtract equation (3) from (4) we have:

$$\begin{gathered} 10x-x=3.33...-0.333... \\ 9x=3 \\ x=\frac{1}{3}[Dividingbothsidesby9] \end{gathered}$$

Step 2: Simplify the expression.

Now substitute values & then evaluate.

$$\begin{gathered} 0.\overline{6}+0.\overline{3}+0.11=\frac{2}{3}+\frac{1}{3}+\frac{11}{100} \\ =\frac{200+100+33}{300} \\ =\frac{333}{300} \\ =1.11 \end{gathered}$$

So, $0.\overline{6}+0.\overline{3}+0.11=1.11$