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Math  /  Numbers & Operations

QuestionSuppose that you find in a reference book that the volume of all the oceans is 1.4×109 km31.4 \times 10^{9} \mathrm{~km}^{3}. To find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. What is this volume in cubic meters?
Express your answer in cubic meters. View Available Hint(s)
Hint 1. Find the conversion factor □\square 1.4×109 km3=1.4 \times 10^{9} \mathrm{~km}^{3}= □\square m3\mathrm{m}^{3}

Studdy Solution

STEP 1

1. We are given the volume of all the oceans as 1.4×109 km31.4 \times 10^{9} \mathrm{~km}^{3}.
2. We need to convert this volume from cubic kilometers to cubic meters.
3. The conversion factor between kilometers and meters is 1 km=1000 m1 \text{ km} = 1000 \text{ m}.
4. Therefore, 1 km3=(1000 m)3=109 m31 \text{ km}^3 = (1000 \text{ m})^3 = 10^9 \text{ m}^3.

STEP 2

1. Identify the conversion factor between cubic kilometers and cubic meters.
2. Apply the conversion factor to the given volume in cubic kilometers to find the volume in cubic meters.

STEP 3

Identify the conversion factor between cubic kilometers and cubic meters.
1 km3=(1000 m)3=109 m3 1 \text{ km}^3 = (1000 \text{ m})^3 = 10^9 \text{ m}^3

STEP 4

Apply the conversion factor to the given volume in cubic kilometers.
Given volume: 1.4×109 km31.4 \times 10^{9} \mathrm{~km}^{3}
Convert to cubic meters: 1.4×109 km3×109 m3/ km3=1.4×1018 m3 1.4 \times 10^{9} \mathrm{~km}^{3} \times 10^{9} \mathrm{~m}^{3}/\mathrm{~km}^{3} = 1.4 \times 10^{18} \mathrm{~m}^{3}
The volume of all the oceans in cubic meters is: 1.4×1018 m3 1.4 \times 10^{18} \mathrm{~m}^{3}

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