Question

express the distance 3,200,000 meters using scientific notation in meters and then in millimeters.
the distance 3,200,000 meters is expressed as meters in scientific notation. (use scientific notation. use the multiplication symbol in the math palette as needed.)

Explanation:

Step1: Recall scientific - notation form

Scientific notation is of the form $a\times10^{n}$, where $1\leqslant|a|\lt10$ and $n$ is an integer.

Step2: Convert 3200000 meters to scientific notation in meters

For 3200000, move the decimal point 6 places to the left to get $a = 3.2$ and $n=6$. So, in meters, it is $3.2\times 10^{6}$ meters.

Step3: Convert meters to millimeters

Since 1 meter = 1000 millimeters = $1\times10^{3}$ millimeters, then 3200000 meters = $3200000\times1000$ millimeters.

Step4: Calculate in scientific - notation for millimeters

$3200000\times1000=3.2\times 10^{6}\times10^{3}$. Using the rule $a^{m}\times a^{n}=a^{m + n}$, we have $3.2\times10^{6 + 3}=3.2\times10^{9}$ millimeters.

Answer:

In meters: $3.2\times 10^{6}$ meters; In millimeters: $3.2\times 10^{9}$ millimeters