Big numbers

How many natural numbers less than 10 to the sixth can be written in numbers: a) 9.8.7 b) 9.8.0

Correct answer:

a =  1092
b =  728

Step-by-step explanation:

$$\begin{gathered} n_1=10^6=1000000 \\ 0<n<n_1 \\ a=3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3+3\cdot 3\cdot 3\cdot 3\cdot 3+3\cdot 3\cdot 3\cdot 3+3\cdot 3\cdot 3+3\cdot 3+3=1092 \end{gathered}$$

$b=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3+2\cdot 3\cdot 3\cdot 3\cdot 3+2\cdot 3\cdot 3\cdot 3+2\cdot 3\cdot 3+2\cdot 3+2=728$

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