Mike and Beth both write the decimal 0.8 (0.88888...)as a fraction. Mike: 45 Beth: 89 Which student wrote the correct fraction? How do you know that student is correct? Describe a mistake that could have been made by the student who wrote the incorrect fraction. (5 points)

Accepted Solution

Answer:see the explanationStep-by-step explanation:we have0.888...This is a repeating decimal (Is a decimal that has a digit, or a block of digits, that repeat over and over and over again without ever ending)Convert to fraction numberLetx=0.888...10x=8.888...Subtract 0.888... from 8.888... to remove the decimal10x-x=8.888...-0.888...9x=8Solve for xx=8/9thereforeMike fraction is incorrectbecause 4/5=0.80.8 is a terminating decimal (It's a decimal with a finite number of digits)Mike's mistake was considering the number as a terminating decimal instead of a repeating decimalBeth is correct becauseIf you divide 8/9the result is 0.8888888...