Problems for Intermediate Methods in Theoretical Physics Edward F. Redish

Books on CD

The standard media for distributing computer information these days is a CD that can hold about 700 MegaBytes (7 x 108 Bytes) of data.   Given that one English character (letter, number, etc.) requires 1 Byte of storage space, estimate how many novels can be stored on a single CD. Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading will be mostly based on your reasoning, not on your answer.

Solution

To do this, we need to have an estimate for the number of characters in a book. Let's do this by first estimating the number of pages in a book, the number of lines on a page, and the number of characters in a line.

number of pages in a typical book ~ 250
(I have in mind a paperback mystery novel -- one of my typical reads.)

number of lines per page ~ 25
(I looked at the lines in the problem and estimated how many blocks of those lines would it take to fill a page 8 inches long)

number of characters per line ~ 80
(I counted the characters -- including spaces and carriage returns -- in the text above to about 5 inches, a typical paperback's width.)

This says the number of characters in a book is about

(250 pages/book) x (25 lines/page) x (80 characters/line)
= (1000/4) x (100/4) x 4/5 (100) characters/book
= 1/20 x 107 characters/book
= (5/102) x 107 characters/book = 5 x 105 characters/book.

Dividing this into the total number of bytes available gives the number of books:

[7 x 108 bytes/CD] / [5 x 105 bytes/book] = 7/5 x 103 books/CD ~ 1400 books/CD.

[GRADING PATTERN: Getting the number of pages within a factor of two was worth 3 pts. Getting the number of characters per page (again within a factor of two) was worth 5. Explanations about where you got the information from was worth 2 more. Note that if you chose a different size book, it was OK if you explained what kind of book you were talking about. The calculation was worth 5 points. If your answer was to three of more significant figures, you were docked 2 points.]

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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120
Email: redish@umd.edu

Last revision 19. October, 2005.