11 Homework

Question #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

Question #2

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

Question #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.

Question #4

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

1. 1. STROKE: | | | | | | | | | | | | | | | |
   2. Tally: [latex]\cancel{||||}\cancel{||||}\cancel{||||} |||[/latex]
   3. Roman: MCMLXII
   4. Roman: DCCXLIV
   5. Roman: [latex]\overline{\overline{\text{IV}}}\overline{\text{CCX}}[/latex]DLI
   6. Egyptian:

      𓁨 𓂭 𓂭 𓁨 𓆼 ∩ ∩ 𓁨 𓂭

   7. Chinese:

      四

      千

      六

      十

      三

1. 8. Mayan:

      𝋧

      𝋠

      𝋰

      𝋣

   9. [latex]4032_{\text{seven}}[/latex]
   10. [latex]\text{T}6\text{W}_{\text{thirteen}}[/latex]
   11. [latex]1 111 001 011_{\text{two}}[/latex]
   12. [latex]507_{\text{nine}}[/latex]

Question #5

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

1. Roman
2. Base Seven
3. Egyptian
4. Bast Two
5. Chinese

Question #6

Convert 838 to:

1. Base Twelve
2. Base Eight
3. Base Five
4. Mayan

Question #7

Convert 13,595 to Base Twelve

Question #8

Convert 120,258 to Mayan

Question #9

Count from 620 to 630 in Base Five

Question #10

State the numeral that comes just before:

1. [latex]173 425 760_{\text{eleven}}[/latex]
2. [latex]2 010 212 000_{\text{four}}[/latex]

Question #11

State the numeral that comes right after:

1. [latex]539100\text{TE}_{\text{twelve}}[/latex]
2. [latex]3102313444_{\text{five}}[/latex]

Question #12

Answer true or false. If false, explain why

1. [latex]2_{\text{four}} = 2[/latex]
2. [latex]3_{\text{four}} = 3_{\text{twelve}}[/latex]
3.  [latex]10_{\text{twelve}} = 10_{\text{five}}[/latex]

Question #13

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

1. Base Three?
2. Base Ten?

Question #14

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

1. [latex]3 \times 7^{8} + 6 \times 7^{5} + 4 \times 7^{4}[/latex] to Base Seven
2. [latex]1 \times 3^{10} + 2 \times 3^{9} + 2 \times 3^{3}[/latex] to Base Three

Question #15

Write each number in expanded notation:

1. [latex]200050030000_{\text{nine}}[/latex]
2. [latex]1 000100001000_{\text{two}}[/latex]

Question #16

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

1. [latex]43.3_{\text{nine}}[/latex]
2. [latex]35.12_{\text{six}}[/latex]
3. [latex]121.21_{\text{three}}[/latex]
4. [latex]333.333_{\text{five}}[/latex]

Question #17

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

1. [latex]3 \times 4^{2} + 2 \times 4^{0} + 3 \times 4^{-1} + 1 \times 4^{-3}[/latex]
2. [latex]5 \times 11^{3} + 10 \times 11^{1} + 8 \times 11^{-1} + 1 \times 11^{-2}[/latex]
3. [latex]1 \times 2^{2} + 1 \times 2^{0} + 1 \times 2^{-1} + 1 \times 2^{-4}[/latex]