Question

rewrite the following statement using a number in scientific notation. my new music player has a capacity of 310 gigabytes. (recall that giga means billion.) my new music player has a capacity of (square) bytes. (use scientific notation. use the multiplication symbol in the math palette as needed.)

Explanation:

Step1: Recall the definition of scientific notation

Scientific notation is of the form $a\times10^{n}$, where $1\leqslant a < 10$ and $n$ is an integer.

Step2: Convert 310 gigabytes to bytes

Since 1 gigabyte = $10^{9}$ bytes, then 310 gigabytes = $310\times10^{9}$ bytes.

Step3: Rewrite in scientific - notation

$310\times10^{9}=(3.1\times10^{2})\times10^{9}$.

Step4: Use the exponent rule $a^{m}\times a^{n}=a^{m + n}$

$(3.1\times10^{2})\times10^{9}=3.1\times10^{2 + 9}=3.1\times10^{11}$ bytes.

Answer:

$3.1\times10^{11}$ bytes