Introduction

In our last lecture, we discussed how the goal of measurement is not just to get a number, but to communicate a value with honesty and precision. This problem set is your first opportunity to practice using the formal rules—dimensional analysis and significant figures—that allow scientists to achieve that goal.

Problems

1. {"partTitle"=>"Part A: Foundational Skills", "instructions"=>"Complete the following problems, showing all work and paying close attention to units and significant figures.", "skillCategories"=>[{"categoryTitle"=>"Dimensional Analysis", "problems"=>[{"problemNumber"=>1, "text"=>"The cheetah is the fastest land animal, capable of running at speeds of up to $120.0 \\ \\text{km/hr}$. What is this speed in meters per second $(\\text{m/s})$?"}, {"problemNumber"=>2, "text"=>"The official height of a basketball hoop is $10.00 \\ \\text{ft}$. What is this height in meters?", "note"=>"Use the conversion factor: $1.000 \\ \\text{in} = 2.540 \\ \\text{cm}$"}, {"problemNumber"=>3, "text"=>"A marathon is a race that is $26.22 \\ \\text{mi}$ long. How many kilometers is this?", "note"=>"Use the conversion factor: $1.000 \\ \\text{mi} = 1.609 \\ \\text{km}$"}]}, {"categoryTitle"=>"Significant Figures", "problems"=>[{"problemNumber"=>4, "text"=>"Calculate the area of a rectangular plot of land that measures $24.5 \\ \\text{m}$ long by $8.2 \\ \\text{m}$ wide."}, {"problemNumber"=>5, "text"=>"A student measures three consecutive displacements: $15.88 \\ \\text{m}$, $2.1 \\ \\text{m}$, and $105 \\ \\text{m}$. What is the total displacement?"}, {"problemNumber"=>6, "text"=>"An experimenter measures a time of $150.0 \\ \\text{s}$. A second experimenter measures $0.55 \\ \\text{s}$. You need to divide the first measurement by the second. What is the result?"}]}]}
2. {"partTitle"=>"Part B: Application & Synthesis", "instructions"=>"The following problem requires you to synthesize multiple skills and connect them to our unit's anchoring phenomenon.", "problems"=>[{"problemNumber"=>7, "text"=>"In the Hexagon Lab, we learned that Eratosthenes measured the distance between the cities of Syene and Alexandria. A modern analysis suggests this distance was approximately $5.00 \\times 10^3$ stadia. If one stadium is equivalent to $185 \\ \\text{m}$, what is the distance between the two cities in kilometers?", "note"=>"Be sure your final answer is reported with the correct number of significant figures."}]}
3. {"partTitle"=>"Part C: Reflection", "instructions"=>"Answer the following question in 2-3 complete sentences in your research log. This question is not about calculation; it is about thinking like a scientist.", "problems"=>[{"problemNumber"=>8, "text"=>"In the problem above, you calculated the distance between the cities. Why would it be scientifically dishonest for you to report that distance with seven significant figures (e.g., $925.1234 \\ \\text{km}$), even if that's what your calculator showed? Connect your answer to the principles of honest and precise measurement we discussed in our last lecture."}]}