It depends where you live! The problem is the definition of 'billion'.
Traditionally, in England a billion was 'a million million' while in the US it was 'a thousand million'. (So much easier to be a billionaire in the US!)
For other countries that speak English, it largely depended which of the two had the greatest influence on their historical development. In Australia for example, up to the nineteen seventies, the English English definition was used. Then at one stage the official position was that the word should not be used at all (in order to avoid confusion). Today, the US English definition is generally accepted. Because of the influence of the media, and things like United Nations population studies etc using the US definition, that is the most likely to be understood in your country, especially by the media (but you'd need to check official standards to be absolutely sure).
So if a billion is a thousand million, then 100 billion is
100 x 1000 000 000 = 100 000 000 000 i.e. 12 digits.
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10
203
This can be solved by looking at each set of digit lengths. From 1 through 9, it's obvious there are 9 digits. From 10 through 99, there are 2 digits for each of the 90 numbers, so that makes 90*2=180 digits. Next, from 100 to 400, there are 401 numbers with 3 digits each, making another 401*3=1,203 digits. So the final answer is 9+180+1,203 = 1,392 digits.
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