How many zeroes are there between 1 and 1 trillion?

Question

Would it be easier if I had asked, "How many 9's are there between 1-100?" See this question:

http://answers.yahoo.com/question/index;_ylt=AkJay6wHimMniniNwiQNoxXsy6IX?qid=20070621153633AAyMknV&show=7#profile-info-terPrihiaa

It's tough to pick one "best answer" when two answerers have it right, iluxa and emucompboy. What to do?

I think the easier way to figure this out is to first count up all the zeroes for numbers that include zeroes in front of them, including 000,000,000,000. The total is obviously 1,200,000,000,000 zeroes. Then you subtract the zeroes on the left side of those numbers, which is easy to add up. Hence, 1,200,000,000,000 - 111,111,111,111 = 1,088,888,888,889.

Answer 1

let's see...

between 1 and 9 - 0 times
between 10 and 99 - 9 times
between 100 and 999: 180 times
- 9 times what's between 100 and 199, and that is
- 10 times in second position, 10 times in first position =20

between 1000 and 9999: 2700
- 9 times what's between 1000 and 1999, and that is
- 100 times in first position, 100 times in second position, 100 times in third position = 300

pattern:

between 10^n and 10^(n+1)-1:
9*( n * 10^(n-1) ) =


trillion = 10^12, and it has 12 zeroes itself.
so the number of zeros is

12 +
9*( 11 * 10^(10) ) +
9*( 10 * 10^(9) ) +
9*( 9 * 10^(8) ) +
... +
9*(1 * 1)

=

9 * (11*10^10 + 10*10^9 + 9*10^8 + ... + 1) + 12 =

1,088,888,888,901

heh, there's more than a trillion zeroes in there!

Answer 2

12

Answer 3

Wow. I am just blown away by this question.
Let's see. First let's assume you're including 1 trillion, so between 1 and 1 trillion inclusive:
For every ten there's one zero.
That means there's 100,000,000,000 from tens.
For every hundred, there's an additional zero.
So there's 10,000,000,000 from hundreds.
Thousand, an additional.
1,000,000,000 from thousands.
I am starting to see a pattern here!
The answer is 111,111,111,111.
If you don't want to include the 1 trillion, then the answer would be 111,111,111,111 - 12.

Edit: Oops, I am so wrong. I forgot to add in "embedded" zeroes. I suck at math!

Answer 4

Discounting leading zeroes, from 1 to 9,999,999,999 I figure there are 9 * 987,654,321 zeroes. Unfortunately, then my nice little pattern falls apart, so I can't go all the way to 1 trillion. Wouldn't you rather know the answer in base 12?

Answer 5

I am not sure how accurate I have been with my calculations but the number 0 appears about 37,286,253,554 times between 1 and 1,000,000,000,000.

edit....Dang, I forgot the embedded 0 also.......lol

Answer 6

Since I assume this is a trick question, I'm going to say none. e

Answer 7

hmm 10000000