If approximately 70% of the Earth's surface is covered with water, what is the order of magnitude for the number of raindrops in the world's oceans?
Hint: The order of magnitude of 2478=2.478×10^3 is 3.
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To find the order of magnitude for the number of raindrops in the world's oceans, we can follow these steps:
1. Determine the approximate volume of the world's oceans. According to the hint, approximately 70% of the Earth's surface is covered with water. Since the oceans make up a significant portion of this water, we can use this percentage as an estimate. The Earth's surface area is approximately 510 million square kilometers. So, the total volume of the oceans can be roughly estimated as 0.7 times this surface area.
Volume of oceans = 0.7 × 510 million square kilometers
2. Convert the volume to cubic meters. To do this, we need to convert the surface area from square kilometers to square meters. Since 1 square kilometer is equal to 1,000,000 square meters, we can multiply the volume by 1,000,000 to get it in cubic meters.
Volume of oceans = 0.7 × 510 million × 1,000,000 cubic meters
3. Estimate the average size of a raindrop. While raindrops can vary in size, we can assume an average size for the purpose of this estimation. Let's say the average size is approximately 1 milliliter, which is equivalent to 0.001 cubic meters.
Average raindrop size = 0.001 cubic meters
4. Divide the volume of the oceans by the average size of a raindrop to find the approximate number of raindrops.
Number of raindrops = (Volume of oceans) / (Average raindrop size)
5. Finally, determine the order of magnitude by converting the result to scientific notation. The order of magnitude is determined by placing the decimal point after the first significant digit and adjusting the exponent accordingly.
For example, if the number of raindrops is 5,670,000 (5.67 million), the order of magnitude is 7 since it can be written as 5.67 × 10^7.
By following these steps and using the appropriate estimations, you can find the order of magnitude for the number of raindrops in the world's oceans.