• Dezimalzahlen
  • ttry-Katalog
  • 06.10.2020
  • Mathematik
  • 6
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  • 1
    Schreibe die Dezimalzahlen als Brüche. Gehe dabei Schrittweise vor wie in dem Beispiel auf der rechten Seite.
    Beispiel:7,15=7+15100=7+320=14020+320=14320\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \text{Beispiel:} \\ 7{,}15 = 7 + \frac{15}{100} \\ = 7 + \frac{3}{20} = \frac{140}{20} + \frac{3}{20} \\ = \frac{143}{20}

    Um auf die Nachkommaziffern zugreifen zu können, werden sie durch eine zweistellige Zufallsvariable gebildet.

    • 7,65=7+65100=7+1320=14020+1320=15320\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 7{,}65 = \cloze{7} + \cloze{\frac{65}{100}} = \cloze{7} + \cloze{\frac{13}{20}} = \cloze{\frac{140}{20}} + \cloze{\frac{13}{20}} = \cloze{\frac{153}{20}}
    • 2,02=2+2100=2+150=10050+150=10150\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 2{,}02 = \cloze{2} + \cloze{\frac{2}{100}} = \cloze{2} + \cloze{\frac{1}{50}} = \cloze{\frac{100}{50}} + \cloze{\frac{1}{50}} = \cloze{\frac{101}{50}}
    • 9,15=9+15100=9+320=18020+320=18320\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 9{,}15 = \cloze{9} + \cloze{\frac{15}{100}} = \cloze{9} + \cloze{\frac{3}{20}} = \cloze{\frac{180}{20}} + \cloze{\frac{3}{20}} = \cloze{\frac{183}{20}}
    • 7,48=7+48100=7+1225=17525+1225=18725\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 7{,}48 = \cloze{7} + \cloze{\frac{48}{100}} = \cloze{7} + \cloze{\frac{12}{25}} = \cloze{\frac{175}{25}} + \cloze{\frac{12}{25}} = \cloze{\frac{187}{25}}
    • 6,64=6+64100=6+1625=15025+1625=16625\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 6{,}64 = \cloze{6} + \cloze{\frac{64}{100}} = \cloze{6} + \cloze{\frac{16}{25}} = \cloze{\frac{150}{25}} + \cloze{\frac{16}{25}} = \cloze{\frac{166}{25}}
    2
    Wandle nun auf dieselbe Art und Weise die gegebenen Brüche schrittweise in Dezimalzahlen um.
    • 8925=7525+1425=3+1425=3+56100=3,56\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{89}{25} = \cloze{\frac{75}{25}} + \cloze{\frac{14}{25}} = \cloze{3} + \cloze{\frac{14}{25}} = \cloze{3} + \cloze{\frac{56}{100}} = \cloze{3{,}56}
    • 41350=40050+1350=8+1350=8+26100=8,26\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{413}{50} = \cloze{\frac{400}{50}} + \cloze{\frac{13}{50}} = \cloze{8} + \cloze{\frac{13}{50}} = \cloze{8} + \cloze{\frac{26}{100}} = \cloze{8{,}26}
    • 24750=20050+4750=4+4750=4+94100=4,94\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{247}{50} = \cloze{\frac{200}{50}} + \cloze{\frac{47}{50}} = \cloze{4} + \cloze{\frac{47}{50}} = \cloze{4} + \cloze{\frac{94}{100}} = \cloze{4{,}94}
    • 623100=600100+23100=6+23100=6+23100=6,23\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{623}{100} = \cloze{\frac{600}{100}} + \cloze{\frac{23}{100}} = \cloze{6} + \cloze{\frac{23}{100}} = \cloze{6} + \cloze{\frac{23}{100}} = \cloze{6{,}23}
    • 135=105+35=2+35=2+60100=2,60\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} \frac{13}{5} = \cloze{\frac{10}{5}} + \cloze{\frac{3}{5}} = \cloze{2} + \cloze{\frac{3}{5}} = \cloze{2} + \cloze{\frac{60}{100}} = \cloze{2{,}60}
  • 3
    Schreibe in der angegebenen Einheit!
    • 174 m 88 cm=174,88 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 174 \text{ m } 88 \text{ cm} = \cloze{174{,}88} \text{ m}
    • 86 m 39 cm=86,39 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 86 \text{ m } 39 \text{ cm} = \cloze{86{,}39} \text{ m}
    • 146 m 29 cm=146,29 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 146 \text{ m } 29 \text{ cm} = \cloze{146{,}29} \text{ m}
    • 181 m 4 cm=181,04 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 181 \text{ m } 4 \text{ cm} = \cloze{181{,}04} \text{ m}
    • 84 m 2 cm=84,02 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 84 \text{ m } 2 \text{ cm} = \cloze{84{,}02} \text{ m}
    • 9 m 55 cm=9,55 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 9 \text{ m } 55 \text{ cm} = \cloze{9{,}55} \text{ m}
    4
    Schreibe in der angegebenen Einheit!
    • 147 € 1 ct=147,01\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 147 \text{ € } 1 \text{ ct} = \cloze{147{,}01} €
    • 94 € 52 ct=94,52\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 94 \text{ € } 52 \text{ ct} = \cloze{94{,}52} €
    • 41 € 4 ct=41,04\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 41 \text{ € } 4 \text{ ct} = \cloze{41{,}04} €
    • 58 € 7 ct=58,07\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 58 \text{ € } 7 \text{ ct} = \cloze{58{,}07} €
    • 59 € 97 ct=59,97\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 59 \text{ € } 97 \text{ ct} = \cloze{59{,}97} €
    • 190 € 32 ct=190,32\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 190 \text{ € } 32 \text{ ct} = \cloze{190{,}32} €

    Ein-, zwei- und dreistellige Nachkommaziffern werden hier in getrennten Variablen gewürfelt, um sie gleichberechtigt erscheinen zu lassen.

    5
    Schreibe in der angegebenen Einheit!
    • 14 kg 86 g=14,086 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 14 \text{ kg } 86 \text{ g} = \cloze{14{,}086} \text{ kg}
    • 170 kg 3 g=170,003 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 170 \text{ kg } 3 \text{ g} = \cloze{170{,}003} \text{ kg}
    • 171 kg 863 g=171,863 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 171 \text{ kg } 863 \text{ g} = \cloze{171{,}863} \text{ kg}
    • 120 kg 330 g=120,330 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 120 \text{ kg } 330 \text{ g} = \cloze{120{,}330} \text{ kg}
    • 132 kg 2 g=132,002 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 132 \text{ kg } 2 \text{ g} = \cloze{132{,}002} \text{ kg}
    • 2 kg 93 g=2,093 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 2 \text{ kg } 93 \text{ g} = \cloze{2{,}093} \text{ kg}
    6
    Schreibe in der angegebenen Einheit!
    • 56  84 m=56,084 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 56 ~\ell~ 84 \text{ m} \ell = \cloze{56{,}084} ~\ell
    • 114  5 m=114,005 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 114 ~\ell~ 5 \text{ m} \ell = \cloze{114{,}005} ~\ell
    • 90  754 m=90,754 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 90 ~\ell~ 754 \text{ m} \ell = \cloze{90{,}754} ~\ell
    • 175  4 m=175,004 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 175 ~\ell~ 4 \text{ m} \ell = \cloze{175{,}004} ~\ell
    • 87  596 m=87,596 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 87 ~\ell~ 596 \text{ m} \ell = \cloze{87{,}596} ~\ell
    • 38  28 m=38,028 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 38 ~\ell~ 28 \text{ m} \ell = \cloze{38{,}028} ~\ell

    Mischung der Aufgaben 3-6

    7
    Schreibe in der angegebenen Einheit!
    • 56  316 m=56,316 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 56 ~\ell~ 316 \text{ m} \ell = \cloze{56{,}316} ~\ell
    • 163 m 15 cm=163,15 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 163 \text{ m } 15 \text{ cm} = \cloze{163{,}15} \text{ m}
    • 125 kg 384 g=125,384 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 125 \text{ kg } 384 \text{ g} = \cloze{125{,}384} \text{ kg}
    • 173 kg 121 g=173,121 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 173 \text{ kg } 121 \text{ g} = \cloze{173{,}121} \text{ kg}
    • 61 € 58 ct=61,58 €\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 61 \text{ € } 58 \text{ ct} = \cloze{61{,}58} \text{ €}
    • 17  778 m=17,778 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 17 ~\ell~ 778 \text{ m} \ell = \cloze{17{,}778} ~\ell
    • 128 kg 69 g=128,069 kg\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 128 \text{ kg } 69 \text{ g} = \cloze{128{,}069} \text{ kg}
    • 142 € 39 ct=142,39 €\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 142 \text{ € } 39 \text{ ct} = \cloze{142{,}39} \text{ €}
    • 42 m 75 cm=42,75 m\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 42 \text{ m } 75 \text{ cm} = \cloze{42{,}75} \text{ m}
    • 72  988 m=72,988 \gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 72 ~\ell~ 988 \text{ m} \ell = \cloze{72{,}988} ~\ell