The speed of an aircraft is 1.024 × 10^3 km/h. Express the distance it would travel in 2 hours 40 minutes in scientific notation.
The Correct Answer and Explanation is:
To determine the distance the aircraft would travel in 2 hours and 40 minutes, let’s break it down into steps:
Step 1: Convert 2 hours and 40 minutes into hours
We know that 40 minutes is a fraction of an hour. To convert 40 minutes to hours:40 minutes=4060 hours=0.6667 hours\text{40 minutes} = \frac{40}{60} \text{ hours} = 0.6667 \text{ hours}40 minutes=6040 hours=0.6667 hours
So, the total time in hours is:Total time=2 hours+0.6667 hours=2.6667 hours\text{Total time} = 2 \text{ hours} + 0.6667 \text{ hours} = 2.6667 \text{ hours}Total time=2 hours+0.6667 hours=2.6667 hours
Step 2: Calculate the distance traveled
The formula to calculate distance is:Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}Distance=Speed×Time
We are given the speed of the aircraft as 1.024×103 km/h1.024 \times 10^3 \, \text{km/h}1.024×103km/h, and the time as 2.6667 hours. Plugging these values into the formula:Distance=1.024×103 km/h×2.6667 hours\text{Distance} = 1.024 \times 10^3 \, \text{km/h} \times 2.6667 \, \text{hours}Distance=1.024×103km/h×2.6667hoursDistance=2.725×103 km\text{Distance} = 2.725 \times 10^3 \, \text{km}Distance=2.725×103km
Step 3: Express in scientific notation
The result is already in scientific notation, but we need to express it in a more standard format:Distance=2.725×103 km\text{Distance} = 2.725 \times 10^3 \, \text{km}Distance=2.725×103km
Thus, the distance the aircraft will travel in 2 hours and 40 minutes is 2.725×103 km2.725 \times 10^3 \, \text{km}2.725×103km.
Final Answer:
2.725×103 km\boxed{2.725 \times 10^3 \, \text{km}}2.725×103km
This result means the aircraft will travel approximately 2,725 kilometers in 2 hours and 40 minutes.
