Papier falten: 0.1 mm => 0,2 mm => 0,4 mm => 0,8 mm => 1,6 mm = 3.2 mm ...
Nach 5 mal falten => 3,2 mm h = $${\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{5}}} = {\frac{{\mathtt{16}}}{{\mathtt{5}}}} = {\mathtt{3.2}}$$ mm
Nach 50 mal falten => h = $${\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}} = {\mathtt{112\,589\,990\,684\,262.4}}$$ mm
= $${\frac{{\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}}}{{\mathtt{1\,000\,000}}}} = {\mathtt{112\,589\,990.684\: \!262\: \!4}}$$ km !!!
Antwort:
Nach 50 mal falten hat man eine Höhe von knapp 112 589 991 km erreicht !
$${\frac{{\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}}}{\left({\mathtt{1\,000\,000}}{\mathtt{\,\times\,}}{\mathtt{40\,000}}\right)}} = {\mathtt{2\,814.749\: \!767\: \!106\: \!56}}$$ mal um die Erde !!!
Etwa 2815 mal um die Erde !
Was schätzt du? Wie oft kann man eine Zeitungsseite maximal falten ?
Papier falten: 0.1 mm => 0,2 mm => 0,4 mm => 0,8 mm => 1,6 mm = 3.2 mm ...
Nach 5 mal falten => 3,2 mm h = $${\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{5}}} = {\frac{{\mathtt{16}}}{{\mathtt{5}}}} = {\mathtt{3.2}}$$ mm
Nach 50 mal falten => h = $${\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}} = {\mathtt{112\,589\,990\,684\,262.4}}$$ mm
= $${\frac{{\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}}}{{\mathtt{1\,000\,000}}}} = {\mathtt{112\,589\,990.684\: \!262\: \!4}}$$ km !!!
Antwort:
Nach 50 mal falten hat man eine Höhe von knapp 112 589 991 km erreicht !
$${\frac{{\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}}}{\left({\mathtt{1\,000\,000}}{\mathtt{\,\times\,}}{\mathtt{40\,000}}\right)}} = {\mathtt{2\,814.749\: \!767\: \!106\: \!56}}$$ mal um die Erde !!!
Etwa 2815 mal um die Erde !
Was schätzt du? Wie oft kann man eine Zeitungsseite maximal falten ?
+14538 
!
