convert 0.8... to a rational number

Answer 1

To convert 0.8... (0.8888...) to a rational number, we can set it equal to a variable x and solve for x.

x = 0.8...

Multiplying both sides of the equation by 10 gives:

10x = 8.8...

Subtracting the equation x = 0.8... from 10x = 8.8... gives:

10x - x = 8.8... - 0.8...

Simplifying the equation gives:

9x = 8

Dividing both sides by 9 gives:

x = 8/9

Therefore, 0.8... is equal to the rational number 8/9.