On February 21, 2001, the Library of Congress' database contained 40 terabytes of data. How many CD's would you need to hold that data?

Assume that the data cannot be compressed and a CD can be filled to capacity.

Conversion figures

1 kilobyte = 1,024 bytes

1 megabyte = 1,024 kilobytes

1 gigabyte = 1,024 megabytes

1 terabyte = 1,024 gigabytes

1 CD = 650 MB of data

Find the number of CD's required for this data. You must create and use variables for conversion.

Example: If 12 apples = 1 orange,

> apples:=12;

> 5*apples;

We find that 5 oranges is 60 apples.

Solution:

> bytes:=1; #Create variables for conversion.

> kilobytes:=1024*bytes;

> megabytes:=1024*kilobytes;

> gigabytes:=1024*megabytes;

> terabytes:=1024*gigabytes;

> cd:=650*megabytes;

Now that we have our conversion factors set up, we can solve the problem. (Note: your variables' names don't matter. It does matter that you set up variables for each conversion unit and used them to form new conversion units.)

> loc:=40*terabytes; #Let's see how many bytes are in 40 terabytes and store the value into a variable called loc.

> cds:=loc/cd; #Let's see how many CD's it would take

> cds:=evalf(cds); #Not very helpful. Let's convert it to a decimal.

According to Maple, you would need 64527.75 CD's. But, the last time I checked, you can't chop a CD into sections. Therefore we need to round up. You can do that in your head, or Maple has some commands to help. (Note: If you are this far, good! Now, you are not expected to know how to round in Maple. I am showing you here for informational purposes only.)

> ceil(cds); #Computes the next highest integer from 64527.75.

The Library of Congress would need 64528 CD's to hold its data.

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