• Prozentzahlen
  • ttry-Katalog
  • 06.10.2020
  • Mathematik
  • 5, 6
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  • Prozentzahlen und Dezimalzahlen

    1
    Fülle die Lücken.
    • 0,5=50%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \cloze{0{,}5} = 5 0 \%
    • 0,7=70%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}7 = \cloze{7 0} \%
    • 0,8=80%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \cloze{0{,}8} = 8 0 \%
    • 0,3=30%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \cloze{0{,}3} = 3 0 \%
    • 0,5=50%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}5 = \cloze{5 0} \%
    • 0,2=20%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}2 = \cloze{2 0} \%
    • 0,6=60%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}6 = \cloze{6 0} \%
    • 0,4=40%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}4 = \cloze{4 0} \%
    • 0,9=90%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \cloze{0{,}9} = 9 0 \%
    2
    Schreibe als Prozentzahl.
    • 0,01=1%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}01 = \cloze{1} \%
    • 0,05=5%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}05 = \cloze{5} \%
    • 0,88=88%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}88 = \cloze{88} \%
    • 0,65=65%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}65 = \cloze{65} \%
    • 0,84=84%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}84 = \cloze{84} \%
    • 0,04=4%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}04 = \cloze{4} \%

    Hier kommen zunächst nur ganze Prozentzahlen vor. Durch die beiden Textausgaben lassen sich ein- und zweistellige Prozentzahlen mit gleicher Wahrscheinlichkeit generieren.

    3
    Schreibe als Kommazahl.
    • 8%=0,08\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 8 \% = \cloze{0{,}08}
    • 4%=0,04\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 4 \% = \cloze{0{,}04}
    • 9%=0,09\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 9 \% = \cloze{0{,}09}
    • 63%=0,63\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 63 \% = \cloze{0{,}63}
    • 74%=0,74\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 74 \% = \cloze{0{,}74}
    • 85%=0,85\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 85 \% = \cloze{0{,}85}
    4
    Schreibe als Prozentzahl.
    • 0,839=83,9%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}839 = \cloze{83{,}9} \%
    • 0,9754=97,54%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}9754 = \cloze{97{,}54} \%
    • 0,5991=59,91%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}5991 = \cloze{59{,}91} \%
    • 0,0878=8,78%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}0878 = \cloze{8{,}78} \%
    • 0,668=66,8%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}668 = \cloze{66{,}8} \%
    • 0,032=3,2%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}032 = \cloze{3{,}2} \%
    • 0,816=81,6%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}816 = \cloze{81{,}6} \%
    • 0,028=2,8%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 0{,}028 = \cloze{2{,}8} \%

    Hier werden die Prozentzahlen gebrochen ausgegeben.

    5
    Schreibe als Dezimalzahl.
    • 4,63%=0,0463\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 4{,}63 \% = \cloze{0{,}0463}
    • 93,3%=0,933\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 93{,}3 \% = \cloze{0{,}933}
    • 7,3%=0,073\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 7{,}3 \% = \cloze{0{,}073}
    • 3,64%=0,0364\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 3{,}64 \% = \cloze{0{,}0364}
    • 16,6%=0,166\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 16{,}6 \% = \cloze{0{,}166}
    • 69,67%=0,6967\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 69{,}67 \% = \cloze{0{,}6967}
    • 37,1%=0,371\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 37{,}1 \% = \cloze{0{,}371}
    • 72,54%=0,7254\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 72{,}54 \% = \cloze{0{,}7254}

    Man beachte die angepassten Nachkommastellen bei den #d-Variablen.

  • Prozentzahlen und Brüche

    6
    Schreibe als Prozentzahl.
    • 710=70%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{7}{10} = \cloze{7 0} \%
    • 210=20%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{2}{10} = \cloze{2 0} \%
    • 110=10%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{1}{10} = \cloze{1 0} \%
    • 910=90%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{9}{10} = \cloze{9 0} \%
    • 810=80%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{8}{10} = \cloze{8 0} \%
    • 410=40%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{4}{10} = \cloze{4 0} \%

    Die Prozentzahlen in den nächsten beiden Aufgaben sind entweder Vielfache von 5 oder von 2. Dadurch können die Brüche in jedem Fall gekürzt werden.

    7
    Schreibe die Prozentzahl zunächst als Dezimalbruch und kürze dann soweit wie möglich.
    • 42%=42100=2150\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 42 \% = \frac{ \cloze{42} }{100} = \cloze{ \frac{21}{50} }
    • 10%=10100=110\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 10 \% = \frac{ \cloze{10} }{100} = \cloze{ \frac{1}{10} }
    • 55%=55100=1120\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 55 \% = \frac{ \cloze{55} }{100} = \cloze{ \frac{11}{20} }
    • 80%=80100=45\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 80 \% = \frac{ \cloze{80} }{100} = \cloze{ \frac{4}{5} }
    • 34%=34100=1750\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 34 \% = \frac{ \cloze{34} }{100} = \cloze{ \frac{17}{50} }
    • 32%=32100=825\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 32 \% = \frac{ \cloze{32} }{100} = \cloze{ \frac{8}{25} }
    • 56%=56100=1425\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 56 \% = \frac{ \cloze{56} }{100} = \cloze{ \frac{14}{25} }
    • 65%=65100=1320\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 65 \% = \frac{ \cloze{65} }{100} = \cloze{ \frac{13}{20} }
    • 20%=20100=15\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 20 \% = \frac{ \cloze{20} }{100} = \cloze{ \frac{1}{5} }
    8
    Erweitere den Bruch zunächst auf Hundertstel und schreibe dann als Prozentzahl.
    • 1320=65100=65%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{13}{20} = \frac{ \cloze{65} }{100} = \cloze{65} \%
    • 320=15100=15%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{3}{20} = \frac{ \cloze{15} }{100} = \cloze{15} \%
    • 110=10100=10%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{1}{10} = \frac{ \cloze{10} }{100} = \cloze{10} \%
    • 1720=85100=85%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{17}{20} = \frac{ \cloze{85} }{100} = \cloze{85} \%
    • 120=5100=5%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{1}{20} = \frac{ \cloze{5} }{100} = \cloze{5} \%
    • 14=25100=25%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{1}{4} = \frac{ \cloze{25} }{100} = \cloze{25} \%
    • 2325=92100=92%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{23}{25} = \frac{ \cloze{92} }{100} = \cloze{92} \%
    • 15=20100=20%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{1}{5} = \frac{ \cloze{20} }{100} = \cloze{20} \%
    • 25=40100=40%\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{2}{5} = \frac{ \cloze{40} }{100} = \cloze{40} \%