Question

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 1

Answer:

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

Step-by-step explanation:

Given

$World\ Ocean: 1.4 * 10^9 km^3$

$Bucket: 20,000 cm^3$

$1 km^3 = 10^{15} cm^3$

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

$Number = \frac{Ocean\ Size}{Bucket\ Size}$

$Number = \frac{1.4 * 10^9 km^3}{20,000cm^3}$

Expand the numerator

$Number = \frac{1.4 * 10^9 * 1km^3}{20,000cm^3}$

Recall that $1 km^3 = 10^{15} cm^3$

So, the expression becomes

$Number = \frac{1.4 * 10^9 * 10^{15} cm^3}{20,000cm^3}$

Simplify the numerator using laws of indices

$Number = \frac{1.4 * 10^{9+15} cm^3}{20,000cm^3}$

$Number = \frac{1.4 * 10^{25} cm^3}{20,000cm^3}$

Expand the denominator

$Number = \frac{1.4 * 10^{25} cm^3}{2 * 10,000cm^3}$

$Number = \frac{1.4 * 10^{25} cm^3}{2 * 10^4\ cm^3}$

Split fraction

$Number = \frac{1.4}{2} * \frac{10^{25} cm^3}{10^4\ cm^3}$

$Number = 0.7 * \frac{10^{25}}{10^4\ }$

Simplify fraction using laws of indices

$Number = 0.7 * 10^{25-4}$

$Number = 0.7 * 10^{21}$

$Number = 7 * 10^{20}$

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