Question

how many kilometers in 2500. yards? however, they all showed different work. student a $2500.\text{ yds} \times\frac{3\text{ ft}}{1\text{ yd}}\times\frac{1\text{ mile}}{5280\text{ ft}}\times\frac{1.609\text{ km}}{1\text{ mile}}=$ student b $2500.\text{ yds} \times\frac{3\text{ ft}}{1\text{ yd}}\times\frac{12\text{ in}}{1\text{ ft}}\times\frac{2.54\text{ cm}}{1\text{ in}}\times\frac{1\text{ km}}{10^{5}\text{ cm}}=$ student c $2500.\text{ yds} \times\frac{3\text{ ft}}{1\text{ yd}}\times\frac{12\text{ in}}{1\text{ ft}}\times\frac{1\text{ m}}{39.37\text{ in}}\times\frac{1\text{ km}}{10^{3}\text{ m}}=$ based on their dimensional analysis, which student or students solved the problem correctly? (note: on the exam you will need to show work on all conversion problems with dimensional analysis.) a. all three solved in correctly. b. students b and c solved it correctly. c. student a and c solved it correctly. d. none of them solved it correctly. e. student a solved it correctly. question 2 how many ounces are in 487 dag? a. 1.72 oz

Explanation:

Step1: Analyze Student A's work

Student A uses the conversions: 1 yard = 3 feet, 5280 feet = 1 mile, 1 mile = 1.609 km. The dimensional - analysis is set up correctly as the units cancel out properly. Starting with yards, the feet and mile units cancel out, leaving kilometers.
\[2500\ yds\times\frac{3\ ft}{1\ yd}\times\frac{1\ mile}{5280\ ft}\times\frac{1.609\ km}{1\ mile}\]

Step2: Analyze Student B's work

Student B uses the conversions: 1 yard = 3 feet, 1 foot = 12 inches, 1 inch = 2.54 cm, \(1\ km = 10^{5}\ cm\). The dimensional - analysis is set up correctly. The yard, foot, inch, and centimeter units cancel out, leaving kilometers.
\[2500\ yds\times\frac{3\ ft}{1\ yd}\times\frac{12\ in}{1\ ft}\times\frac{2.54\ cm}{1\ in}\times\frac{1\ km}{10^{5}\ cm}\]

Step3: Analyze Student C's work

Student C uses the conversions: 1 yard = 3 feet, 1 foot = 12 inches, 39.37 inches = 1 meter, \(1\ km = 10^{3}\ m\). The dimensional - analysis is set up correctly. The yard, foot, inch, and meter units cancel out, leaving kilometers.
\[2500\ yds\times\frac{3\ ft}{1\ yd}\times\frac{12\ in}{1\ ft}\times\frac{1\ m}{39.37\ in}\times\frac{1\ km}{10^{3}\ m}\]

Answer:

a. All three solved it correctly.