Question

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)

Answer 1

see the explanation

Explanation:

we have

0.888...

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 number

Let

x=0.888...

10x=8.888...

Subtract 0.888... from 8.888... to remove the decimal

10x-x=8.888...-0.888...

9x=8

Solve for x

x=8/9

therefore

Mike fraction is incorrect

because 4/5=0.8

0.8 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 decimal

Beth is correct

because

If you divide 8/9

the result is 0.8888888...