There are approximately 330,000,000 cubic miles of water on Earth. A cubic mile is approximately 147,200,000,000 cubic feet. How much water is on Earth? Estimate using scientific n... There are approximately 330,000,000 cubic miles of water on Earth. A cubic mile is approximately 147,200,000,000 cubic feet. How much water is on Earth? Estimate using scientific notation. Read more

Steps to Solve

1. Convert cubic miles to cubic feet

To convert the volume from cubic miles to cubic feet, we use the given conversion factor: 1 cubic mile = 147,200,000,000 cubic feet.

Thus, we can calculate the volume in cubic feet as follows:

$$ \text{Volume in } ft^3 = 330,000,000 \text{ cubic miles} \times 147,200,000,000 \text{ ft}^3/\text{mile}^3 $$

2. Perform the multiplication

Now, we perform the multiplication step-by-step.

First, we can express the numbers in scientific notation for easier calculation:

• Convert 330,000,000 to scientific notation: $$ 330,000,000 = 3.3 \times 10^8 $$

• Convert 147,200,000,000 to scientific notation: $$ 147,200,000,000 = 1.472 \times 10^{11} $$

So we can rewrite the volume equation as:

$$ \text{Volume in } ft^3 = (3.3 \times 10^8) \times (1.472 \times 10^{11}) $$

3. Multiply the coefficients and add the exponents

Now, we multiply the coefficients (3.3 and 1.472) and add the exponents:

$$ 3.3 \times 1.472 \approx 4.8576 $$

Add the exponents:

$$ 8 + 11 = 19 $$

So the volume becomes:

$$ \text{Volume in } ft^3 \approx 4.8576 \times 10^{19} $$

4. Round to a suitable number of significant figures

Finally, we round the result to one significant figure:

$$ \approx 5 \times 10^{19} \text{ ft}^3 $$