How many seconds are there in a month of 30 days? Express it in scientific notation. The radius of the earth is
km. Write the value of this scientific
The Correct Answer and Explanation is:
Answer:
- Number of seconds in a 30-day month:
30 days×24 hours/day×60 minutes/hour×60 seconds/minute=2,592,000 seconds30 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 2,592,000 \text{ seconds}30 days×24 hours/day×60 minutes/hour×60 seconds/minute=2,592,000 seconds
Expressed in scientific notation:2.592×106 seconds2.592 \times 10^6 \text{ seconds}2.592×106 seconds
- Radius of Earth (commonly accepted average value):
Radius of Earth=6,371 km\text{Radius of Earth} = 6,371 \text{ km}Radius of Earth=6,371 km
In scientific notation:6.371×103 km6.371 \times 10^3 \text{ km}6.371×103 km
Explanation
Time is a measurable quantity that can be broken into smaller units. A standard month with 30 days has hours, minutes and seconds. To convert this duration into seconds, a step-by-step multiplication is applied, starting from days to hours, then minutes and finally seconds.
Each day has 24 hours. Each of those hours includes 60 minutes. Each minute is made up of 60 seconds. Therefore, multiplying all these values together for 30 days gives:
30 × 24 = 720 hours
720 × 60 = 43,200 minutes
43,200 × 60 = 2,592,000 seconds
The result, 2,592,000 seconds, is a large number. Scientific notation helps express large or small quantities more compactly. To convert 2,592,000 into scientific notation, move the decimal point left until only one digit remains on its left. In this case, the decimal is moved 6 places to the left, resulting in 2.592 × 10⁶.
Next, consider the Earth’s radius. This value is an average because the Earth is not a perfect sphere but slightly flattened at the poles. The equatorial radius is slightly larger than the polar radius, but for most general calculations, the average radius of 6,371 kilometers is used. Just like with time, scientific notation offers a simpler form to express this. Shifting the decimal point three positions left turns 6,371 into 6.371 × 10³ kilometers.
Using scientific notation helps in performing mathematical operations more efficiently and ensures easier understanding of very large or very small values.
