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  • 06.10.2020
  • Mathematik
  • 5, 6
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  • Konstruktion der Rundungsfunktion

    Die Math.js-Funktionen floor() und ceil() runden nur auf ganze Zahlen, und das unabhängig von der ersten Nachkommastelle. Das schulmäßige Auf- und Abrunden (auch auf andere Stellen, z.B. Zehntel) muss daher selbst konstruiert werden.

    1
    Runde auf Zehner.
    • 83988400\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 839 8 \approx \cloze{840 0}
    • 19021900\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 190 2 \approx \cloze{190 0}
    • 673670\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 67 3 \approx \cloze{67 0}
    • 94069410\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 940 6 \approx \cloze{941 0}
    • 144140\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 14 4 \approx \cloze{14 0}
    • 59956000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 599 5 \approx \cloze{600 0}
    • 643640\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 64 3 \approx \cloze{64 0}
    • 681680\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 68 1 \approx \cloze{68 0}
    • 96179620\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 961 7 \approx \cloze{962 0}
    2
    Runde auf Hunderter.
    • 71187100\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 71 1 8 \approx \cloze{71 00}
    • 16051600\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 16 0 5 \approx \cloze{16 00}
    • 3286132900\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 328 6 1 \approx \cloze{329 00}
    • 9270192700\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 927 0 1 \approx \cloze{927 00}
    • 89398900\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 89 3 9 \approx \cloze{89 00}
    • 62826300\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 62 8 2 \approx \cloze{63 00}
    • 1552615500\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 155 2 6 \approx \cloze{155 00}
    • 69076900\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 69 0 7 \approx \cloze{69 00}
    • 98319800\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 98 3 1 \approx \cloze{98 00}
    3
    Runde auf Tausender.
    • 4798648000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 47 9 8 6 \approx \cloze{48 000}
    • 1922819000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 19 2 2 8 \approx \cloze{19 000}
    • 7713477000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 77 1 3 4 \approx \cloze{77 000}
    • 6088361000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 60 8 8 3 \approx \cloze{61 000}
    • 739833740000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 739 8 3 3 \approx \cloze{740 000}
    • 587279587000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 587 2 7 9 \approx \cloze{587 000}
    • 481227481000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 481 2 2 7 \approx \cloze{481 000}
    • 3662237000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 36 6 2 2 \approx \cloze{37 000}
    • 759122759000\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 759 1 2 2 \approx \cloze{759 000}

    Im Ergebnis werden an die entsprechende Variable die erforderliche Anzahl von Nullen angehängt. Dabei ist es nötig, diese durch ein Leerzeichen abzutrennen, da der Editor sonst eine neue Variable erstellt. Innerhalb der Formel-Umgebung von LaTeX wird dieses Leerzeichen jedoch ignoriert, es entsteht also in der Ausgabe kein Abstand.

    4
    Runde auf ganze Zahlen.
    • 812,6813\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 812, 6 \approx \cloze{813}
    • 546,8547\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 546, 8 \approx \cloze{547}
    • 750,7751\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 750, 7 \approx \cloze{751}
    • 54,5355\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 54, 5 3 \approx \cloze{55}
    • 637,8638\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 637, 8 \approx \cloze{638}
    • 830,3830\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 830 , 3 \approx \cloze{830}
    • 86,1486\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 86 , 1 4 \approx \cloze{86}
    • 43,6744\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 43, 6 7 \approx \cloze{44}
    • 70,3970\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 70 , 3 9 \approx \cloze{70}
  • 5
    Runde auf Zehntel.
    • 236,70236,7\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 236{,}7 0 \approx \cloze{236{,}7}
    • 215,47215,5\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 215{,}4 7 \approx \cloze{215{,}5}
    • 397,22397,2\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 397{,}2 2 \approx \cloze{397{,}2}
    • 701,80701,8\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 701{,}8 0 \approx \cloze{701{,}8}
    • 363,92363,9\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 363{,}9 2 \approx \cloze{363{,}9}
    • 31,28531,3\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 31{,}2 8 5 \approx \cloze{31{,}3}
    • 610,98611,0\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 610{,}9 8 \approx \cloze{611{,}0}
    • 21,88321,9\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 21{,}8 8 3 \approx \cloze{21{,}9}
    • 5,8775,9\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 5{,}8 7 7 \approx \cloze{5{,}9}
    6
    Runde auf Hundertstel.
    • 4,10764,11\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 4{,}10 7 6 \approx \cloze{4{,}11}
    • 76,147676,15\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 76{,}14 7 6 \approx \cloze{76{,}15}
    • 379,247379,25\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 379{,}24 7 \approx \cloze{379{,}25}
    • 42,485542,49\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 42{,}48 5 5 \approx \cloze{42{,}49}
    • 481,542481,54\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 481{,}54 2 \approx \cloze{481{,}54}
    • 82,239682,24\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 82{,}23 9 6 \approx \cloze{82{,}24}
    • 476,451476,45\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 476{,}45 1 \approx \cloze{476{,}45}
    • 83,393283,39\gdef\cloze#1{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}} 83{,}39 3 2 \approx \cloze{83{,}39}