Theory:

The number of repeating decimals in the decimal expansion of the rational number is called the period of the decimal.
Example:
Verify 7=6.9¯
 
Let x=6.9¯=6.9999...
 
As the period of the circle for \(x\) is one(only the number \(9\) repeating), multiply the number by \(10\).
 
We have 10x=69.9999...
 
Subtracting \(x\) from \(10x\),
 
10xx=69.9999...6.999...9x=63x=639x=7
 
Thus, we have x=6.9¯ and x=7. This implies 7=6.9¯.