Question

$0.\overline{5} + 0.19\overline{4}$.

Answer 1

Answer:

$0.\overline{5} + 0.19\overline{4}=0.75$

Step-by-step explanation:

Given expression:

$0.\overline{5} + 0.19\overline{4}$

To evaluate the expression.

Solution.

The values are

$0.\overline{5}=0.555555......$  

Let $X=0.555555.....$ -----------1                  

Multiplying 10 both sides.

$10X=5.555555....$----------2

Subtracting 1 from 2.

 $10X=5.555555....$

- $X=0.555555.....$

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$9X=5.0$

Dividing both sides by 9.

$\frac{9X}{9}=\frac{5}{9}$

$X=\frac{5}{9}$

$0.19\overline{4}=0.194444....$

Let $Y=0.1944444..$

Multiplying both sides by 100

$100Y=19.44444..$------------3

Multiplying 1000 both sides.

$1000Y=194.4444....$----------4

Subtracting 3 from 4.

 $1000Y=194.4444....$

- $100Y=19.44444.....$

-------------------------------------------

$900Y=175.0$

Dividing both sides by 900.

$\frac{900Y}{900}=\frac{175}{900}$

$Y=\frac{175}{900}$

So, we can evaluate the given expression as:

⇒ $0.\overline{5} + 0.19\overline{4}$

⇒ $X+Y$    

⇒ $\frac{5}{9}+\frac{175}{900}$

Taking LCD = 900

⇒ $\frac{5\times 100}{9\times 100}+\frac{175}{900}$

⇒ $\frac{500}{900}+\frac{175}{900}$

Adding numerators.

⇒ $\frac{500+175}{900}$

⇒ $\frac{675}{900}$

⇒ $0.75$ (Answer)