Answer :

kate200468
[tex]0.050505...=?\\\\x=0.50505...\ \ /\cdot100\\\\100x=5.050505...\\-------------\\100x-x=5.050505..-0.050505...\\\\99x=5\ \ /:99\\\\x= \frac{\big{5}}{\big{99}} [/tex]
isyllus

Answer:

[tex]\frac{5}{99}[/tex]

Step-by-step explanation:

We are given a repeating decimal [tex]0.\bar{05}[/tex]

Let x=0.0505050505.......... ---------------eq(1)

We can see two digit is repeating after decimal

So, we multiply by 100 both sides of equation x=0.05050505.... and we get

100x=5.0505050505......... ---------------eq(2)

Subtract  eq(2)-eq(1)

100x-x=5

99x=5

[tex]x=\frac{5}{99}[/tex]

[tex]0.050505..... = \frac{5}{99}[/tex]

Thus, [tex]\frac{5}{99}[/tex] as fraction.