Homework help- How many digits must be written to number the pages of abook that is 576 pages long? How...?

Question

Here is the whole math problem:

How many digits must be written to number the pages of a book that is 576 pages long? How many 7's are used? How many pages have numbers ending in 7?

If you can figure this out, please give me step by step instruction on how you solved it. Thank you!

Answer 1

hard leh

Answer 2

It is simpler to regard all the pages as being 3-digit numbers

(000 - 576), and handle the 1-digit and 2-digit numbers specially,

by disregarding their leading 0's.

Total digits:

3 * 576 - 1 * 90 - 2 * 9 = 1728 - 108 = 1620

(Start with 3 digits per page, deduct 1 for the 2-digit numbers

and 2 for the 1-digit numbers)

Pages ending in 7:

00x - 56x each have a 7, so 57 pages end in 7

Total number of 7's:

no 7's in hundreds' place

57 in the ones' place

that leaves the tens' place:

70-79 occur in the

0xx, 1xx, 2xx, 3xx, 4xx series

so 50 of those, 7 in the 5xx pages

57+57 = 114 total 7's

.

Answer 3

well you consider that the book uses 1 digit for pages 1-9, 2 digits for pages 10-99, and three digits for pages 100-576

thats # of pages 1-9 + # of pages 10-99 (times 2) + # of pages 100-576( times 3) = total digits

you consider that page 7, 17,27,37,47...557,567 each end in 7. and count that total

7,17,27,37,47,57,67,77,87,97= 10 sevens for every length of 100 pages. so thats 40 sevens to reach page 500, then count the remaining pages that end in 7. 507,517,527,537,547,557,567. so you end up with 47 pages that end in 7.

we're aware that 47 sevens have been used. go back and add 1 more 7 for each case of 77 used. so 77,177,277,377,477.  So you get 51 7 used total

Answer

1.?

2. 51

3.47.

Answer 4

Digit count is 9 x 1 + 90 x 2 + 476 x 3.

Number of 7's is 1 + 9 + 10 + 4 x 10 + 4 x 10 + 7 + 7.

Number of trailing 7's is 56.

All of this is done by simple nose count.