Question

directions: show your work using dimensional analysis! highlight and underline your final answer. 11.) calculate the number of feet in a 5 km race, given the following unit equalities: 1 inch = 2.54 cm; 12 inches = 1 ft (3 points)

Explanation:

Step1: Convert km to cm

We know that 1 km = 1000 m and 1 m = 100 cm. So for 5 km, we have $5\ km\times\frac{1000\ m}{1\ km}\times\frac{100\ cm}{1\ m}=5\times10^{5}\ cm$.

Step2: Convert cm to inches

Given 1 inch = 2.54 cm, so the number of inches is $5\times 10^{5}\ cm\times\frac{1\ inch}{2.54\ cm}\approx1.9685\times 10^{5}\ inches$.

Step3: Convert inches to feet

Since 12 inches = 1 ft, the number of feet is $1.9685\times 10^{5}\ inches\times\frac{1\ ft}{12\ inches}\approx16404.2\ ft$.

Answer:

16404.2 ft