# The total volume of the ocean in liters.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.2, Problem 97E
To determine

## The total volume of the ocean in liters.

Expert Solution

The total volume of the ocean is 1.332×1021liters_.

### Explanation of Solution

Given that, the average ocean depth is 3.7×103m and the area of the ocean is 3.6×1014m2.

It is known that, one cubic meter contains 1000 liters.

Substitute 3.6×1014m2 for Area of the ocean and 3.7×103m for Average Ocean Depth in the formula to calculate volume of the ocean as shown below.

Volumeoftheocean=3.6×1014m2×3.7×103m=3.6×1014×3.7×103m3=3.6×3.7×1014×103m3

Use the law of exponents and simplify the above expression,

Volume of the ocean=13.32×1014+3m3     (aman=am+n)=13.32×1017m3

Now, move decimal 1 place to the left and add 1 to the power of 10 to write the above quantity in proper scientific notation as shown below.

Volumeoftheocean=13.32×1017m3=1.332×1018m3

It is known that, 1m3=1000liters.

Use the above unit conversion of m3 into liters to convert volume of the ocean in m3 into liters as shown below.

Volumeoftheocean=1.332×1018m3=1.332×1018×1m3=1.322×1018×1000liters=1.322×1018×103liters

Use the law of exponents and further simplify the above expression.

Volume of the ocean=1.322×1018×103liters=1.332×1018+3liters=1.332×1021liters

Therefore, the total volume of the ocean is 1.332×1021liters_.

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