Need help to solve the Mathematical problem
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Need help to solve the Mathematical problem

[From: ] [author: ] [Date: 12-11-29] [Hit: ]
pls help with the detailed steps to solve.Thanks in advance.-On pages 1 - 9,On pages 10 - 99, that is a total of 90 pages, but,......
A story book has 100 pages altogether. How many digits are used to print all the page numbers in the story book? The answer is 192, but do not know the steps to attain this solution, pls help with the detailed steps to solve. Thanks in advance.

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On pages 1 - 9, that is a total of 9 digits or 9 single numbers

On pages 10 - 99, that is a total of 90 pages, but, remember that these now two digits since it now takes two numbers to display the page. So it takes 90*2 = 180 digits

On page 100, we have 3 digits because it is 3 numbers.

Add them up:

9 + 180 + 3 = 192

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Pages 1 to 9 have all 1digits and they are 9 in all .
So, total digits from 1 to 9 = 9 .......(1)

Now, pages 10 to 99 have 2 digits and they are 90 in all .
So, total digits from 10 to 99 = 2*90 = 180 .........(2)

Again, page 100 has 3 digits ............(3)

Now, from (1) , (2) and (3),we sum up
9+180+3 = 192 (Ans.)

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There are 9 pages that have 1 digit. --> (9 x 1)
>>because of pages 1 to 9

There are 90 pages that have 2 digits --> (90 x 2)
>> because of pages 10 to 99

There is 1 page with 3 digits --> (3 x 1)
>> because of page 100

add it all up:

(1 x 9) + (2 x 90) + (3 x 1)
= 9 + 180 + 3
=192

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Let's see, there are 10 digits, 0 through 9.
1..9, that's 9
10..19, that's 20
20..29, 20 again, so 20, 9 times for the 30s, 40s, all the way to the 90s, or 180, plus the first 9 pages, 189, and three more digits for page 100.
192.

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Pages 1 to 9 each use 1 digit for their page number: sub-total = 9 digits

Pages 10 to 99 each use 2 digits for their page number: sub-total 90*2 = 180 digits

Page 100 use 3 digits: sub-total - 3 digits

Total number digits used = 9 + 180 + 3 = 192 digits

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