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The world's oceans hold roughly 1.4 x 109 cubic kilometers of water. A typical bucket holds roughly 20,000 cubic centimeters of water. If there are 1015 cubic centimeters in a cubic kilometer, how many bucketloads would it take to empty the world's oceans?

Answer :

MrRoyal

Answer:

It'll take a bucket loads of [tex]7 * 10^{20}[/tex] to empty world's ocean

Step-by-step explanation:

Given

[tex]World\ Ocean: 1.4 * 10^9 km^3[/tex]

[tex]Bucket: 20,000 cm^3[/tex]

[tex]1 km^3 = 10^{15} cm^3[/tex]

To get the number of bucket loads, we simply divide the size of the ocean by the size of the bucket;

[tex]Number = \frac{Ocean\ Size}{Bucket\ Size}[/tex]

[tex]Number = \frac{1.4 * 10^9 km^3}{20,000cm^3}[/tex]

Expand the numerator

[tex]Number = \frac{1.4 * 10^9 * 1km^3}{20,000cm^3}[/tex]

Recall that [tex]1 km^3 = 10^{15} cm^3[/tex]

So, the expression becomes

[tex]Number = \frac{1.4 * 10^9 * 10^{15} cm^3}{20,000cm^3}[/tex]

Simplify the numerator using laws of indices

[tex]Number = \frac{1.4 * 10^{9+15} cm^3}{20,000cm^3}[/tex]

[tex]Number = \frac{1.4 * 10^{25} cm^3}{20,000cm^3}[/tex]

Expand the denominator

[tex]Number = \frac{1.4 * 10^{25} cm^3}{2 * 10,000cm^3}[/tex]

[tex]Number = \frac{1.4 * 10^{25} cm^3}{2 * 10^4\ cm^3}[/tex]

Split fraction

[tex]Number = \frac{1.4}{2} * \frac{10^{25} cm^3}{10^4\ cm^3}[/tex]

[tex]Number = 0.7 * \frac{10^{25}}{10^4\ }[/tex]

Simplify fraction using laws of indices

[tex]Number = 0.7 * 10^{25-4}[/tex]

[tex]Number = 0.7 * 10^{21}[/tex]

[tex]Number = 7 * 10^{20}[/tex]

Hence, it'll take a bucket loads of [tex]7 * 10^{20}[/tex] to empty world's ocean

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