0.999... = 1
True or False?
true
illustration
1/3 = .3333....
2/3 = .6666.....
add them
3/3 = .99999......
1 = .99999....
true
x = 0.9999999...
10x = 9.9999999...
subtract to get
9x = 9
x = 1
True.
To understand why 0.999... equals 1, we can use mathematical observations.
Let's assume the decimal representation of 0.999... is denoted as x.
Now, if we multiply both sides of the equation x = 0.999... by 10, we get 10x = 9.999...
Now, if we subtract x from 10x, we have:
10x - x = 9.999... - 0.999...
Simplifying this, we get:
9x = 9
Dividing both sides of the equation by 9:
x = 1
Hence, we have proved that x, which represents the decimal 0.999..., is equal to 1.