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.
To convert the decimal 2.55555555.. to a fraction, we can observe that the digit 5 repeats infinitely. This can be denoted as a repeating decimal: 2.5555... = 2.5¯.
Using the fraction bar notation, we can set up an equation to solve for x:
x = 2.5¯
Multiplying both sides of the equation by 10 to shift the decimal point one place to the right:
10x = 25.5¯
Subtracting the original equation from the shifted equation, we can eliminate the repeating decimal:
10x - x = 25.5 - 2.5
9x = 23
To get the fraction form, we divide both sides of the equation by 9:
x = 23/9
Therefore, the correct fraction representation for 2.55555555.. is 23/9.