Skip to main content
Mathematics LibreTexts

3.6: Homework

  • Page ID
    82993
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    • Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
    • Start a new module on the front side of a new page and write the module number on the top center of the page.
    • Answers without supporting work will receive no credit.
    • Some solutions are given in the solutions manual.
    • You may work with classmates but do your own work.

    HW #1

    For each two sets noted, indicate whether or not the sets match. If they do, show a matching. If they do not, explain why not.

    a. Small Blue A-blocks and Large Red A-Blocks

    b. Yellow A-blocks and Circular A-blocks

    HW #2

    Describe a matching between the set of counting numbers, {1, 2, 3, ...} and the set of positive multiples of five, {5, 10, 15, ...}.

    HW #3

    Show every possible one-to-one correspondence between the Small Blue A-blocks and the Small Red A-blocks. Use abbreviations or pictures to denote the blocks.

    HW #4

    Convert each numeral to a Hindu-Arabic Base Ten numeral.

    a. STROKE: | | | | | | | | | | | | | | | |
    b. Tally: \(\cancel{||||}\cancel{||||}\cancel{||||} |||\)
    c. Roman: MCMLXII
    d. Roman: DCCXLIV
    e. Roman: \(\bar{\bar{\text{IV}}\text{CCX}}\)DLI

    f. Egyptian:

    Screen Shot 2021-04-20 at 12.24.30 AM.png

    g. Chinese

    Screen Shot 2021-04-20 at 12.25.38 AM.png

    h. Mayan

    Screen Shot 2021-04-20 at 12.26.38 AM.png
    i. \(4032_{\text{seven}}\)
    j. \(T6W_{\text{thirteen}}\)
    k. \(1 \ 111 \ 001 \ 011_{\text{two}}\)
    l. \(507_{\text{nine}}\)

    HW #5

    Convert 342 to a numeral in the numeration system or base specified.

    a. Roman b. Base Seven c. Egyptian
    d. Base Two e. Chinese

    HW #6

    Convert 838 to:

    a. Base Twelve b. Base Eight
    c. Base Five d. Mayan

    HW #7

    Convert 13,595 to Base Twelve

    HW #8

    Convert 120,258 to Mayan

    HW #9

    Count from 620 to 630 in Base Five

    HW #10

    State the numeral that comes just before:

    a. \(173 \ 425 \ 760_{\text{eleven}}\) b. \(2 \ 010 \ 212 \ 000_{\text{four}}\)

    HW #11

    State the numeral that comes right after:

    a. \(539100TE_{\text{twelve}}\) b. \(3 \ 102 \ 313 \ 444_{\text{five}}\)

    HW #12

    Answer true or false. If false, explain why

    a. \(2_{\text{four}} = 2\) b. \(3_{\text{four}} = 3_{\text{twelve}}\) c. \(10_{\text{twelve}} = 10_{\text{five}}\)

    HW #13

    Using Base Three blocks, you had 7 flats, 10 longs and 5 units. What number does this represent in

    a. Base Three? b. Base Ten?

    HW #14

    Write each number shown in expanded notation as a numeral in the base specified.

    a. \(3 \times 7^{8} + 6 \times 7^{5} + 4 \times 7^{4}\) to Base Seven
    b. \(1 \times 3^{10} + 2 \times 3^{9} + 2 \times 3^{3}\) to Base Three

    HW #15

    Write each number in expanded notation:

    a. \(200 \ 050 \ 030 \ 000_{\text{nine}}\)
    b. \(1 \ 000 \ 100 \ 001 \ 000_{\text{two}}\)

    HW #16

    Write each numeral in expanded form. Then, convert each numeral to a Base Ten mixed numeral with the fraction simplified.

    a. \(43.3_{\text{nine}}\) b. \(35.12_{\text{six}}\)
    c. \(121.21_{\text{three}}\) d. \(333.333_{\text{five}}\)

    HW #17

    Rewrite from expanded form to a numeral in the appropriate base.

    a. \(3 \times 4^{2} + 2 \times 4^{0} + 3 \times 4^{-1} + 1 \times 4^{-3}\)
    b. \(5 \times 11^{3} + 10 \times 11^{1} + 8 \times 11^{-1} + 1 \times 11^{-2}\)
    c. \(1 \times 2^{2} + 1 x\times 2^{0} + 1 \times 2^{-1} + 1 \times 2^{-4}\)

    This page titled 3.6: Homework is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Julie Harland via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.