Eric's notebook has 30 pages. He wants to write a number on each page. How many digits will he write when he numbers all the pages in the notebook?
1 Answer
Eric will need 51 digits.
Explanation:
The question is a bit ambiguous, since we don't know if there are any restrictions on which numbers Eric can write. But if we assume he will number the pages 1 to 30, then the number of digits he'll need is found as follows:
Each number from 1 to 9 is only one digit long. So he'll need
#stackrel("num. digits")overbrace1 xx stackrel("range to cover")overbrace("("9-1)+stackrel("inclusive")overbrace"1)"=9#
9 digits to write those 9 numbers. (Our subtotal so far is 9.)
"Inclusive" just means "don't ignore the first number". The difference between 9 and 1 is 8, but there are 9 numbers between 9 and 1 inclusive, so we add 1 as shown.
Each number from 10 to 30 is two digits long. That means Eric will need
#2 xx (30-10+1)" "=" "2 xx 21" "=" "42#
42 digits to write those 21 numbers. Thus, our grand total number of digits is
#9 + 42 = 51#
51 digits.
Note:
Be careful to avoid the trap of thinking "digits" and "numbers" are the same thing. Just like how you use letters to make words, you use digits to make numbers. (And just like some words are only one letter, some numbers are only one digit.)
