Convert the following repeating decimal to a fraction in simplest form.
point, 2, start overline, 1, end overline
.2
1
To convert the repeating decimal .2̅ (or .21̅) to a fraction, we can set it equal to x and subtract the original number from 100 times x to eliminate the repeating part.
Let's first call .2̅, x.
x = .2̅
We multiply both sides of the equation by 10 to move the decimal point to the right:
10x = 2.̅
Now, we subtract the original equation from the new equation:
10x - x = 2.̅ - .2̅
This gives us:
9x = 2
Dividing both sides of the equation by 9:
x = 2/9
Thus, the repeating decimal .2̅ is equal to the fraction 2/9 in simplest form.