Convert the following repeating decimal to a fraction in simplest form.
point, 9, start overline, 1, end overline
.9
1
To convert the repeating decimal .9̅ to a fraction, we can assign a variable ‘x’ to it and perform a simple algebraic manipulation.
Let x = .9̅
Multiplying both sides of the equation by 10, we get:
10x = 9.9̅
Next, we subtract x from 10x:
10x - x = 9.9̅ - .9̅
This simplifies to:
9x = 9
Dividing both sides of the equation by 9:
9x/9 = 9/9
The 9’s on the left side of the equation cancel out, leaving us with:
x = 1
Therefore, the repeating decimal .9̅ is equivalent to the fraction 1 in simplest form.