Escreve sob a forma de dízima
Números reais: Matematicamente Falando 8 - Pág. 35 Ex. 11
Escreve sob a forma de dízima finita, através da fração decimal, ou sob a forma de dízima infinita periódica, utilizando o algoritmo da divisão, os seguintes números, identificando o período e o comprimento do período das dízimas infinitas.
| \[\frac{3}{8}\] | \[ – \frac{8}{3}\] | \[\frac{{13}}{5}\] | \[ – \frac{{13}}{8}\] |
| \[\frac{{12}}{7}\] | \[\frac{{128}}{{72}}\] | \[\frac{{13}}{{80}}\] | \[\frac{{72}}{{25}}\] |
A aplicação do algoritmo da divisão está no final da página.
| Dízima finita | Dízima infinita periódica | Período | Comprimento do período | ||
| A | \[\frac{3}{8} = \frac{3}{{{2^3}}} \times \frac{{{5^3}}}{{{5^3}}} = \frac{{375}}{{1000}} = 0,375\] | x | |||
| B | \[ – \frac{8}{3} = – 2,\left( 6 \right)\] | x | \[6\] | \[1\] | |
| C | \[\frac{{13}}{5} = \frac{{13}}{5} \times \frac{2}{2} = \frac{{26}}{{10}} = 2,6\] | x | |||
| D | \[ – \frac{{13}}{8} = – \frac{{13}}{{{2^3}}} \times \frac{{{5^3}}}{{{5^3}}} = – \frac{{1625}}{{1000}} = – 1,625\] | x | |||
| E | \[\frac{{12}}{7} = {\rm{1}}{\rm{,}}\left( {{\rm{714285}}} \right)\] | x | \[{{\rm{714285}}}\] | \[6\] | |
| F | \[\frac{{128}}{{72}} = \frac{{{2^7}}}{{{2^3} \times {3^2}}} = \frac{{{2^4}}}{{{3^2}}} = \frac{{16}}{9} = 1,\left( 7 \right)\] | x | \[7\] | \[1\] | |
| G | \[\frac{{13}}{{80}} = \frac{{13}}{{{2^4} \times 5}} \times \frac{{{5^3}}}{{{5^3}}} = \frac{{1625}}{{10000}} = 0,1625\] | x | |||
| H | \[\frac{{72}}{{25}} = \frac{{72}}{{25}} \times \frac{4}{4} = \frac{{288}}{{100}} = 2,88\] | x |
\[\begin{array}{*{20}{c}}{8,}&0&0&{}&3&{}&{}\\\hline2&0&{}&{}&{2,}&6&6\\{}&2&0&{}&{}&{}&{}\\{}&{}&2&{}&{}&{}&{}\end{array}\]
\[\begin{array}{*{20}{c}}1&{6,}&0&0&{}&9&{}&{}\\\hline{}&7&0&{}&{}&{1,}&7&7\\{}&{}&7&0&{}&{}&{}&{}\\{}&{}&{}&7&{}&{}&{}&{}\end{array}\]
\[\begin{array}{*{20}{c}}1&{2,}&0&0&0&0&0&0&0&0&{}&7&{}&{}&{}&{}&{}&{}&{}&{}\\\hline{}&5&0&{}&{}&{}&{}&{}&{}&{}&{}&{1,}&7&1&4&2&8&5&7&1\\{}&{}&1&0&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\\{}&{}&{}&3&0&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\\{}&{}&{}&{}&2&0&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\\{}&{}&{}&{}&{}&6&0&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\\{}&{}&{}&{}&{}&{}&4&0&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\\{}&{}&{}&{}&{}&{}&{}&5&0&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\\{}&{}&{}&{}&{}&{}&{}&{}&1&0&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\\{}&{}&{}&{}&{}&{}&{}&{}&{}&3&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\end{array}\]
