Skip to main content
Mathematics LibreTexts

18.14: Historical Counting

  • Page ID
    41808
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    1. Partial answer: Jars: 3 singles, 3 @ \(x3, 2\) @ \(x6, 1\) @ \(x12. 3+9+12+12 = 36\)

    3. \(113\)

    5. \(3022\)

    7. \(53\)

    9. \(1100100\)

    11. \(332\)

    13. \(111100010\)

    15. 7,1,10 base \(12=1030\) base 10

    17. 6,4,2 base \(12=914\) base 10

    19. 175 base \(10=1,2,7\) base \(12=\)clipboard_e3b08a678aad9aa453acee9507e89e1dc.png

    21. 10000 base \(10=5,9,5,4\) base \(12=\) clipboard_eabf062c0fe6e87914f5016d4e6288307.png

    23. \(135=6,15\) base \(20=\)clipboard_ea43fbfa8342f95aa3047371e1eef834a.png

    25. \(360=18,0\) base \(20=\)clipboard_ec33f42587b80e5e757f8bb7ddf74f779.png

    27. \(10500=1,6,5,0\) base 20 clipboard_e0c0e246f276705f7115e699f3d312667.png

    29. 1,2,12 base \(20=452\) base 10

    31. 3,0,3 base \(20=1203\) base 10

    33. \(32+11=1,12_{20}+11_{20}=1,23_{20}=2,3_{20}=43\)

    clipboard_e69975d72d75f98a3d2f99c5c06094ff8.png

    35. \(35+148=1,15_{20}+7,8_{20}=8,23_{20}=9,320=183\)

    clipboard_e30ef9f745fe1a4983c262375034921a0.png

    37. \(450+844=1,2,10_{20}+2,2,4_{20}=3,4,14_{20}=1294\)

    clipboard_e8597bd05fbcb25624d0372ac0bb10db0.png


    This page titled 18.14: Historical Counting is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?