Question

When comparing answers on a group assignment, Jenny and Jeremy found that their answers did not match. Part 1: Who do you believe has the correct solution for the group assignment—Jenny or Jeremy? In two or more complete sentences, explain, in mathematical terms, the reasoning behind your conjecture. Part 2: Use long division to convert the fraction provided in each of the student's answers to a decimal number. Include all of your calculations in your final answer. Part 3: Using complete sentences, compare your conjecture in Part 1 with your results in Part 2. Was your conjecture correct or incorrect?

Answer 1

PART 1:

Jeremy gives the correct answer. 

The value of 0.41 [with a bar over the digit 4 and 1] shows that the digit 4 and 1 are reoccurring = 0.414141414141414141....

Jenny's assumption of 41/100 will give a decimal equivalency of 0.41 [without a bar over digit 4 and 1]. This value is not a reoccurring decimal value. 

PART 2:

The long division method is shown in the picture below

PART 3:

As mentioned in PART 1, the result of converting 41/100 into a decimal is 0.41 [non-reoccuring decimal] while converting 41/99 into a decimal is 0.41414141... [re-occuring decimal]. The conjecture in PART 1 is correct