# [SOLVED] Problem Solving

• Feb 2nd 2009, 01:59 PM
phillyfan09
[SOLVED] Problem Solving
I have solved a problem, but am not so sure if I have the right answer. If anyone can help check it for me and correct what is wrong, if anything, I would greatly appreciate it!

PROBLEM:
Jen has to number the 396 pages in her biology notebook. How many digits will she have to write?

I got the answer 1075 digits by:

pages 1-9 = 9 digits
10-99 = 178 digits (99-10 = 89 #s. 89 x 2 digits = 178)
396-100 = 888 digits (396-100 = 296 #s x 3 digits = 888)

9
178
+ 888
_______
1075 digits on 396 pages

Again, if anyone can help go over this it would be a great help!

Thank you
• Feb 2nd 2009, 02:01 PM
amberkraidich
Correct!
Good job, you got it right.
• Feb 2nd 2009, 02:03 PM
phillyfan09
Great! Thanks!
• Feb 2nd 2009, 10:43 PM
Jhevon
Quote:

Originally Posted by phillyfan09
I have solved a problem, but am not so sure if I have the right answer. If anyone can help check it for me and correct what is wrong, if anything, I would greatly appreciate it!

PROBLEM:
Jen has to number the 396 pages in her biology notebook. How many digits will she have to write?

I got the answer 1075 digits by:

pages 1-9 = 9 digits
10-99 = 178 digits (99-10 = 89 #s. 89 x 2 digits = 178)
396-100 = 888 digits (396-100 = 296 #s x 3 digits = 888)

9
178
+ 888
_______
1075 digits on 396 pages

Again, if anyone can help go over this it would be a great help!

Thank you

actually, there are 90 2-digit #s and 297 3-digit #s (you have to add 1 to include the 10 and the 100 respectively). so the total comes up to 1080
• Feb 3rd 2009, 08:17 AM
phillyfan09
Could you show me how you would work through that?
• Feb 3rd 2009, 11:20 AM
Jhevon
Quote:

Originally Posted by phillyfan09
Could you show me how you would work through that?

think of it this way: how many digits are there between 0 and 9 inclusive? 10 right? do we get 10 simply by saying 9 - 0? now, to include the end points when numbering a list, we compute the difference plus 1. so there are 10 digits in a list of integers from 0 to 9 since we have (9 - 0) + 1 = 10

similarly, going from 10 - 99 for instance, we have (99 - 10) + 1 numbers. the 10 here is like the "0" in my previous example. so you are really counting the numbers as "0, 1, 2, 3, ..." as opposed to "1, 2, 3, ..." that +1 accounts for the "0", that is, the first term in the list.
• Feb 3rd 2009, 04:40 PM
phillyfan09
Thank you!