Final answer:
The student's question involves converting a speed from meters per second to kilometers per hour, ensuring that units are converted correctly and significant figures are maintained. After the proper conversion, the speed is found to be 270 km/h with three significant figures.
Step-by-step explanation:
The student is asking about the conversion of a speed measurement from meters per second (m/s) to kilometers per hour (km/h). To perform this conversion, we multiply by the necessary conversion factors to change meters into kilometers and seconds into hours. Here's the calculation in detail:
rate = 75 m/s × 60 s/min × 1 h/60 min × 10³ km/m
Firstly, cancel out the units correctly to ensure that meters cancel with meters, seconds with seconds, and minutes with minutes. After canceling out appropriate units, you're left with kilometers per hour. Checking the significant figures is the next step in the conversion. Since 75 has two significant figures (the zeroes after 75 are not considered significant because there is no decimal point), the converted speed should also be reported with two significant figures. Lastly, to check if the answer is reasonable, you can evaluate if the speed seems practical, comparing it to common speed values in km/h.
After calculation:
rate = 75 m/s × 60 min/h × 10³ m/km × 1 h/60 min = 270,000 m/h × 1 km/1000 m = 270 km/h
This new speed value of 270 km/h is expressed with three significant figures, aligning with the originally provided value of 75 m/s.