Question

answer the following. (a) the total surface area of europe is approximately 3,930,000 square miles. write this number in scientific notation. (b) the signal from a certain satellite takes approximately 4.1×10^(-3) seconds to reach earth. write this number in standard notation. (a) square miles (b) seconds

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form $a\times 10^{n}$, where $1\leqslant|a|\lt10$ and $n$ is an integer.

Step2: Convert 3,930,000 to scientific notation

Move the decimal point 6 places to the left, so $a = 3.93$ and $n=6$. The number in scientific notation is $3.93\times 10^{6}$ square miles.

Step3: Recall standard - notation rule for scientific notation

For a number in scientific notation $a\times 10^{n}$, if $n\lt0$, we move the decimal point $|n|$ places to the left.

Step4: Convert $4.1\times 10^{-3}$ to standard notation

Since $n=-3$, move the decimal point 3 places to the left. So $4.1\times 10^{-3}=0.0041$ seconds.

Answer:

(a) $3.93\times 10^{6}$ square miles
(b) $0.0041$ seconds