This document discusses calculating the number of digits needed to write out large numbers. It finds that 11 digits are needed for 43,000,000,000. It also calculates that 95 digits are needed for 999, 369,693,100 digits for 9(9)9, 78 digits for (99)9, and 18 digits for 999. It concludes by showing the relative sizes of these numbers.

1. Exercice 34
(a)
N = int(1 + log(43 000 000 000))
= int(1 + 10, 63) = int(11, 63) = 11 chiffres.
(b)
999 → N = int(1 + log(999 )) = int(1 + 99 log(9)) = 95 chiffres
9(9 ) → N = int(1 + log(99 )) = int(1 + 99 log(9))
9 9
= 369 693 100chiffres
(99 )9 → N = int(1 + log(99 )9 ) = int(1 + 81 log(9)) = 78 chiffres
999 → N = int(1 + log(999 )) = int(1 + 9 log(99)) = 18 chiffres
99 )
999 < (99 )9 < 999 < 9(