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 set up the equation:
x = 2.55555555
Multiply both sides by 10 to eliminate the decimal:
10x = 25.5555555
Next, subtract the original equation from the equation multiplied by 10:
10x - x = 25.5555555 - 2.55555555
9x = 23
Simplify:
x = 23/9
This means that the fraction form of 2.55555555 is 23/9, which matches Leo's fraction. Di's fraction of 55/100 is incorrect because it does not simplify to the decimal 2.55555555.