Convert the following repeating decimal to a fraction in simplest form.

Question

point, 9, start overline, 1, end overline
.9
1

Answer 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.