Efetua a decomposição decimal
Números reais: Matematicamente Falando 8 - Pág. 19 Ex. 7
Efetua a decomposição decimal de cada um dos seguintes números:
\[\begin{array}{*{20}{c}}{23,45}&{6,056}&{0,2745}&{9876,42}\end{array}\]
\[\begin{array}{*{20}{r}}{23,4500}& = &{2 \times {{10}^1} + 3 \times {{10}^0} + 4 \times {{10}^{ – 1}} + 5 \times {{10}^{ – 2}} + 0 \times {{10}^{ – 3}} + 0 \times {{10}^{ – 4}}}\\{6,0560}& = &{6 \times {{10}^0} + 0 \times {{10}^{ – 1}} + 5 \times {{10}^{ – 2}} + 6 \times {{10}^{ – 3}} + 0 \times {{10}^{ – 4}}}\\{0,2745}& = &{2 \times {{10}^{ – 1}} + 7 \times {{10}^{ – 2}} + 4 \times {{10}^{ – 3}} + 5 \times {{10}^{ – 4}}}\\{9876,4200}& = &{9 \times {{10}^3} + 8 \times {{10}^2} + 7 \times {{10}^1} + 6 \times {{10}^0} + 4 \times {{10}^{ – 1}} + 2 \times {{10}^{ – 2}} + 0 \times {{10}^{ – 3}} + 0 \times {{10}^{ – 4}}}\\{}&{}&{}\\{}&{}&{{\rm{Simplificando}}\;{\rm{a}}\;{\rm{escrita:}}}\\{}&{}&{}\\{23,45}& = &{2 \times {{10}^1} + 3 \times {{10}^0} + 4 \times {{10}^{ – 1}} + 5 \times {{10}^{ – 2}}}\\{6,056}& = &{6 \times {{10}^0} + 5 \times {{10}^{ – 2}} + 6 \times {{10}^{ – 3}}}\\{0,2745}& = &{2 \times {{10}^{ – 1}} + 7 \times {{10}^{ – 2}} + 4 \times {{10}^{ – 3}}}\\{9876,42}& = &{9 \times {{10}^3} + 8 \times {{10}^2} + 7 \times {{10}^1} + 6 \times {{10}^0} + 4 \times {{10}^{ – 1}} + 2 \times {{10}^{ – 2}}}\end{array}\]
