Question

the volume of the atlantic ocean is about 3.1·10^{17} cubic meters. the mississippi river has an annual flow of 6.3·10^{11} cubic meters. how many times would the annual flow of the mississippi river fit in the atlantic ocean? write your final answer in scientific notation, and round to two decimal places.

Explanation:

Step1: Set up the division

We need to divide the volume of the Atlantic Ocean by the annual - flow of the Mississippi River. The volume of the Atlantic Ocean is $3.1\times10^{17}$ cubic meters and the annual flow of the Mississippi River is $6.3\times10^{11}$ cubic meters. So the calculation is $\frac{3.1\times10^{17}}{6.3\times10^{11}}$.

Step2: Use the quotient - rule of exponents

According to the quotient - rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $a = 3.1$, $b = 6.3$, $m = 17$, and $n = 11$. So $\frac{3.1}{6.3}\times10^{17-11}$.

Step3: Calculate the coefficient and the exponent

First, calculate $\frac{3.1}{6.3}\approx0.492$. Then, $17−11 = 6$. So the result is $0.492\times10^{6}$.

Step4: Convert to proper scientific notation

In scientific notation, the coefficient should be between 1 and 10. So we rewrite $0.492\times10^{6}$ as $4.92\times10^{5}$.

Answer:

$4.92\times10^{5}$