Answer:
[tex]0.\overline{5} + 0.19\overline{4}=0.75[/tex]
Step-by-step explanation:
Given expression:
[tex]0.\overline{5} + 0.19\overline{4}[/tex]
To evaluate the expression.
Solution.
The values are
[tex]0.\overline{5}=0.555555......[/tex]
Let [tex]X=0.555555.....[/tex] -----------1
Multiplying 10 both sides.
[tex]10X=5.555555....[/tex]----------2
Subtracting 1 from 2.
[tex]10X=5.555555....[/tex]
- [tex]X=0.555555.....[/tex]
-------------------------------------------
[tex]9X=5.0[/tex]
Dividing both sides by 9.
[tex]\frac{9X}{9}=\frac{5}{9}[/tex]
[tex]X=\frac{5}{9}[/tex]
[tex]0.19\overline{4}=0.194444....[/tex]
Let [tex]Y=0.1944444..[/tex]
Multiplying both sides by 100
[tex]100Y=19.44444..[/tex]------------3
Multiplying 1000 both sides.
[tex]1000Y=194.4444....[/tex]----------4
Subtracting 3 from 4.
[tex]1000Y=194.4444....[/tex]
- [tex]100Y=19.44444.....[/tex]
-------------------------------------------
[tex]900Y=175.0[/tex]
Dividing both sides by 900.
[tex]\frac{900Y}{900}=\frac{175}{900}[/tex]
[tex]Y=\frac{175}{900}[/tex]
So, we can evaluate the given expression as:
⇒ [tex]0.\overline{5} + 0.19\overline{4}[/tex]
⇒ [tex]X+Y[/tex]
⇒ [tex]\frac{5}{9}+\frac{175}{900}[/tex]
Taking LCD = 900
⇒ [tex]\frac{5\times 100}{9\times 100}+\frac{175}{900}[/tex]
⇒ [tex]\frac{500}{900}+\frac{175}{900}[/tex]
Adding numerators.
⇒ [tex]\frac{500+175}{900}[/tex]
⇒ [tex]\frac{675}{900}[/tex]
⇒ [tex]0.75[/tex] (Answer)
