Question

A futile task is proverbially said to be "like trying to empty the ocean with a teaspoon." Just how futile is such a task? Estimate the number of teaspoonfuls of water in the Earth's oceans.

Short answer

Answer: There are approximately 2.664 * 10^23 teaspoonfuls of water in Earth's oceans.

Step-by-step solution

Find the volume of Earth's oceans

First, we need to find the total volume of Earth's oceans. According to the United States Geological Survey (USGS), the total volume of water in Earth's oceans is approximately 1.332 billion cubic kilometers.

Convert the ocean volume to liters

We will now convert the volume of Earth's oceans from cubic kilometers to liters. We know that 1 cubic kilometer is equal to 1 trillion (10^12) liters. So, we can multiply the ocean's volume, in cubic kilometers, by 10^12 to find the volume in liters: 1.332 * 10^9 (cubic kilometers) * 10^12 (liters per cubic kilometer) = 1.332 * 10^21 liters

Convert the ocean volume to teaspoons

Now, we will convert this volume from liters to teaspoons. We know that 1 liter is equal to 1000 mL, and that there are 5 mL in a teaspoon. Therefore, we can first convert the volume to mL and then divide it by 5 to find the number of teaspoonfuls: (1.332 * 10^21 liters) * (1000 mL per liter) = 1.332 * 10^24 mL Now, we finish the conversion by dividing by 5: (1.332 * 10^24 mL) / 5 (mL per teaspoon) = 2.664 * 10^23 teaspoonfuls The estimated number of teaspoonfuls of water in the Earth's oceans is approximately 2.664 * 10^23 teaspoons. This indeed illustrates the futility of trying to empty the ocean using only a teaspoon.

Key concepts

Volume Conversion

Volume conversion involves changing a measurement of volume from one unit to another. This allows for comparisons and calculations using different systems of measurement. In the case of converting the volume of Earth's oceans, it's essential to start with a known quantity: as per the USGS, the total volume of ocean water is about 1.332 billion cubic kilometers.

To convert this to a more common measurement, like liters, you need to know the conversion factor between cubic kilometers and liters. Since 1 cubic kilometer equals 1 trillion, or \(10^{12}\), liters, you multiply the ocean's volume in cubic kilometers by this factor:

• 1.332 billion cubic kilometers \(\times 10^{12} = 1.332 \times 10^{21}\) liters.

Understanding volume conversion is crucial when dealing with large-scale measurements like entire oceans or small-scale measurements in everyday situations.

Earth's Oceans

Earth's oceans are vast bodies of saltwater that cover about 71% of the Earth's surface. With a combined volume of approximately 1.332 billion cubic kilometers, they play a vital role in supporting life and regulating climate.

Comprehending the enormity of Earth's oceans becomes tangible when broken down into smaller units, like teaspoons. Trying to conceive this involves recognizing how massive these bodies are in comparison to something as small as a teaspoon. Such a perspective can help highlight the vast scales scientists and researchers work with when studying the Earth's environment.

Unit Conversion

Unit conversion is the process of converting different measurement units to understand quantities better. This can involve converting volume, length, mass, and many other units.

Our example involves converting liters into milliliters, and then to teaspoons. Since 1 liter equals 1000 milliliters, you multiply the volume in liters by 1000 to convert to milliliters. To find out how many teaspoons there are, divide the total milliliters by 5 (since 1 teaspoon equals 5 milliliters):

• \(1.332 \times 10^{21}\) liters \(\times 1000 = 1.332 \times 10^{24}\) milliliters.
• \(1.332 \times 10^{24} / 5 = 2.664 \times 10^{23}\) teaspoons.

Through unit conversion, it becomes feasible to make practical comparisons, like determining the number of teaspoonfuls in oceans, which sounds seemingly unimaginable at first glance.

Mathematical Calculation

Mathematical calculations are crucial when performing tasks that involve measurement conversion. These calculations not only require knowledge of basic arithmetic operations, but also the understanding of scientific notation, especially when dealing with extremely large or tiny quantities.

In the context of converting the volume of Earth's oceans, it involves several calculations:

• Using the conversion factor from cubic kilometers to liters, multiply 1.332 billion by \(10^{12}\).
• Convert liters to milliliters by multiplying by 1000.
• Finally, divide the product by 5 to convert milliliters into teaspoons.

An accurate practice of these mathematical steps can help clarify the scale of different measurements, from the immense volume of Earth's oceans to the tiny measurement of a teaspoon.