16. (8.7.14 pp2) how many bucketloads would it take to bucket out the world’s oceans? write your answer in…

16. (8.7.14 pp2) how many bucketloads would it take to bucket out the world’s oceans? write your answer in scientific notation.\nsome useful information:\n- the world’s oceans hold roughly 1.4×10^9 cubic kilometers of water.\n- a typical bucket holds roughly 20,000 cubic centimeters of water.\n- there are 10^15 cubic centimeters in a cubic kilometer.

16. (8.7.14 pp2) how many bucketloads would it take to bucket out the world’s oceans? write your answer in scientific notation.\nsome useful information:\n- the world’s oceans hold roughly 1.4×10^9 cubic kilometers of water.\n- a typical bucket holds roughly 20,000 cubic centimeters of water.\n- there are 10^15 cubic centimeters in a cubic kilometer.

Answer

Explanation:

Step1: Convert ocean volume to cm³

We know the ocean volume is $1.4\times 10^{9}$ km³. Since $1$ km³ = $10^{15}$ cm³, the volume of the ocean in cm³ is $(1.4\times 10^{9})\times10^{15}=1.4\times10^{9 + 15}=1.4\times 10^{24}$ cm³.

Step2: Calculate number of bucket - loads

A bucket holds 20000 cm³ = $2\times 10^{4}$ cm³. Let the number of bucket - loads be $n$. Then $n=\frac{1.4\times 10^{24}}{2\times 10^{4}}$. Using the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $n=\frac{1.4}{2}\times10^{24-4}=0.7\times 10^{20}$. In scientific notation, we rewrite it as $n = 7\times 10^{19}$.

Answer:

$7\times 10^{19}$