Question

1. there are 10 computers in the computer lab that each have 20 gb hard drives. how many bytes (b) of disk space do we have in the computer lab in total.

Explanation:

Step1: Recall the conversion factor

We know that \(1\space\text{GB} = 2^{30}\space\text{bytes}= 1073741824\space\text{bytes}\) (or we can also use the approximation \(1\space\text{GB}\approx10^{9}\space\text{bytes}\), but for accurate calculation we use the binary conversion). Also, first we find the total number of gigabytes and then convert it to bytes.

First, find the total number of gigabytes in the lab. There are 10 computers and each has 20 GB. So total GB \(= 10\times20=200\space\text{GB}\)

Step2: Convert gigabytes to bytes

Now, to convert 200 GB to bytes, we multiply the total number of gigabytes by the number of bytes in one gigabyte.

Using the exact conversion \(1\space\text{GB} = 2^{30}\space\text{bytes}\)

Total bytes \(= 200\times2^{30}\)

\(2^{30}=1073741824\)

So \(200\times1073741824 = 214748364800\space\text{bytes}\)

(If we use the decimal approximation \(1\space\text{GB}\approx10^{9}\space\text{bytes}\), then total bytes \(= 200\times10^{9}=2\times 10^{11}\space\text{bytes}\), but the exact value is \(214748364800\) )

Answer:

The total disk space in bytes is \(214748364800\) (or \(2\times 10^{11}\) if using decimal approximation for GB to bytes conversion)