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

Question

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

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

Leo is correct because a repeating decimal typically has 9s in the denominator

Who is correct and why?

Answer 1

Leo is correct. A repeating decimal can be expressed as a fraction with the repeating digit(s) in the numerator and a denominator of all 9s. In this case, since the decimal 2.55555555.. repeats with the digit 5, it can be written as the fraction 55/99.