Question

Convert the following repeating decimal to a fraction in simplest form.
., start overline, 2, 8, end overline

Answer 1

To convert the repeating decimal ., start overline, 2, 8, end overline to a fraction in simplest form, we can use the concept of geometric series.

Let x be the repeating decimal:
x = 0.282828...

Now, we multiply both sides of the equation by 100:
100x = 28.282828...

Subtracting the first equation from the second equation, we get:
100x - x = 28.282828... - 0.282828...
99x = 28

Dividing both sides of the equation by 99, we find:
x = 28/99

Therefore, the repeating decimal ., start overline, 2, 8, end overline is equivalent to the fraction 28/99 in simplest form.