Di and Leo both write the decimal 2.55555555.. As a fraction.

Di’s fraction: 2 55/100
Leo’s fraction: 2 55/99

Who is correct and why?

1 answer

Leo is correct.

To convert the repeating decimal 2.55555... into a fraction, we can label it as x and solve the equation:

x = 2.555555...

If we multiply both sides of the equation by 10, we get:

10x = 25.555555...

Now, we subtract the first equation (x) from the second equation (10x):

10x - x = 25.555555... - 2.555555...
9x = 23

Dividing both sides of the equation by 9:

9x/9 = 23/9
x = 23/9

Therefore, the correct fraction representation of 2.555555... is 23/9. This matches Leo's fraction of 2 55/99.