Dean ran 5 miles this week and wants to know how many kilometers he ran. His work is below.

Question

StartFraction 5 miles Over 1 EndFraction times StartFraction 1.61 kilometers Over 1 mile EndFraction = 80.5 miles

A 2-column table with 1 row titled Units of Length. Column 1 is labeled Customary System Units with entry 1 mile. Column 2 is labeled Metric System Units with entry 1.61 kilometers.

What are Dean’s errors? Select all that apply.
He has the wrong units in his answer.
Dean should have used two conversion factors.
Dean should have kilometers in the denominator of the conversion factor.
The decimal point in his answer is in the wrong place.

Answer 1

Dean has the following errors in his work:

1. He has the wrong units in his answer. - He incorrectly concludes that 5 miles converts to 80.5 miles, which is not a valid conversion.

2. The decimal point in his answer is in the wrong place. - If he performed the conversion correctly, 5 miles would equal approximately 8.05 kilometers (not 80.5 miles).

Dean's calculation also suggests that he has not converted miles to kilometers properly. He should have obtained the value in kilometers rather than mistakenly arriving at a number with the same unit.

The other two options are not applicable:

• Dean should have used two conversion factors. - This is not necessary; one conversion factor is sufficient for the conversion from miles to kilometers.
• Dean should have kilometers in the denominator of the conversion factor. - This is also not necessary for a single conversion factor; he used the correct structure.

Therefore, the correct selections would be "He has the wrong units in his answer" and "The decimal point in his answer is in the wrong place."