[tex]100 \cdot(0.01 + 0.02 + 0.03 + ... + 0.09) = \\ \\ \\ 100 \cdot( \dfrac{1}{100} + \dfrac{2}{100} + \dfrac{3}{100} + ... + \dfrac{9}{100} ) = \\ \\ \\ 100 \cdot( \dfrac{1 + 2 + 3 + ... + 9}{100} ) = \\ \\ \\ 100 \cdot( \dfrac{9 \times 10 \div 2}{100} ) = \\ \\ \\ 100 \cdot( \dfrac{90 \div 2}{100} ) = \\ \\ \\ 100 \cdot \dfrac{45}{100} = \\ \\ \\ \dfrac{100 \times 45}{100} = \dfrac{4500}{100} ^{ \div 100} = \dfrac{45}{1} = 45[/tex]
