5. 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?
Leo is correct.
Decimals that have digits that repeat infinitely can be represented as fractions using the formula:
x = a / (10^n - 1)
Where "x" is the decimal, "a" is the non-repeating part of the decimal, and "n" is the number of digits in the repeating part.
In this case, Di's fraction can be written as:
2 55' / 100 = 255/100 = 2.55
This fraction does not correctly represent the decimal 2.55555555..
On the other hand, Leo's fraction can be written as:
2 55/99 = 255/99 = 2.55555555..
This fraction correctly represents the decimal 2.55555555.., as it follows the formula for converting repeating decimals into fractions.